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060CCAlg1U2L3ALinearEquationSolvingReview</span></p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <table> <tbody> <tr> <td> <p><span class="s1">A.</span></p> <p><span class="s1">x/3 - 7 = -2</span></p> <p><span class="s1">x/3 = 5</span></p> <p><span class="s1">x = 15</span></p> </td> <td> <p><span class="s1">B.</span></p> <p><span class="s1">4x + 3 = -17</span></p> <p><span class="s1">4x = -20</span></p> <p><span class="s1">x = -5</span></p> </td> <td> <p><span class="s1">C.</span></p> <p><span class="s1">5x + 12 = 87</span></p> <p><span class="s1">x = (87 - 12)/5</span></p> <p><span class="s1">x = 15</span></p> </td> </tr> <tr> <td> <p><span class="s1">D. (x+7)/3 = 2</span></p> <p><span class="s1">x+7 = 6</span></p> <p><span class="s1">x = -1</span></p> </td> <td> <p><span class="s1">E.<span class="Apple-converted-space"></span></span></p> <p><span class="s1">-6 (x-1) = 18</span></p> <p><span class="s1">-6 = 18x - 18</span></p> <p><span class="s1">18x = 12</span></p> <p><span class="s1">x = 12/18</span></p> <p><span class="s1">x = 2/3 = 0.66</span></p> </td> <td> <p><span class="s1">F</span></p> <p><span class="s1">8x + 2 = -2<span class="Apple-converted-space"></span></span></p> <p><span class="s1">8x = -2 -2<span class="Apple-converted-space"></span></span></p> <p><span class="s1">x = -1/2 = -0.5</span></p> </td> </tr> <tr> <td> <p><span class="s1">G</span></p> <p><span class="s1">(3/4)x - 5 = 4</span></p> <p><span class="s1">(3/4)x = 9</span></p> <p><span class="s1">x = 9 * (4/3)</span></p> <p><span class="s1">x = 12</span></p> </td> <td> <p><span class="s1">H</span></p> <p><span class="s1">(-5/2)x + 6 = 1</span></p> <p><span class="s1">(-5/2)x = -5</span></p> <p><span class="s1">x = (-5)/(-5/2)</span></p> <p><span class="s1">x = 2</span></p> </td> <td> <p><span class="s1">I</span></p> <p><span class="s1">6x + 3 = -1</span></p> <p><span class="s1">6x = -4</span></p> <p><span class="s1">x = -(4/6) = -(2/3) = -0.66</span></p> </td> </tr> </tbody> </table> <p><span class="s1"></span> </p> <p><span class="s1">Exercise #2</span></p> <p><span class="s1"></span> </p> <p><span class="s2">5(x-3)</span><span class="s1"> + 2 = 7</span></p> <p><span class="s1"><span class="Apple-converted-space"> </span>8</span></p> <p><span class="s1"></span> </p> <p><span class="s1">5(x-3) + 16 = 56</span></p> <p><span class="s1">5(x-3) = 40</span></p> <p><span class="s1">x-3= 8</span></p> <p><span class="s1">x = 11</span></p> <p><span class="s1"></span> </p> <p><span class="s1"><span class="Apple-converted-space"> </span>Exercise #3</span></p> <p><span class="s1">(a) 5(x-3) + 2x = 4(x+3)</span></p> <p><span class="s1">5x - 15 + 2x = 4x + 12</span></p> <p><span class="s1">7x - 15 = 4x + 12</span></p> <p><span class="s1"></span> </p> <p><span class="s1">(b) 7x - 15 = 4x + 12</span></p> <p><span class="s1">3x = 27</span></p> <p><span class="s1">x = 9</span></p> <p><span class="s1">Let x = 9 for 5(x-3) + 2x = 4(x+3)</span></p> <p><span class="s1">5(9-3) + 2(9) = 4((9)+3)</span></p> <p><span class="s1">30 + 18 = 48</span></p> <p><span class="s1">The equation holds true.</span></p> <p><span class="s1"></span> </p> <p><span class="s1">Exercise #4</span></p> <p><span class="s1">(a) 7(x-2)-3(x+3) = 5(x-3) + x</span></p> <p><span class="s1">7x - 14 - 3x - 9 = 5x - 15 + x</span></p> <p><span class="s1">4x - 23 = 6x - 15</span></p> <p><span class="s1">2x = -8</span></p> <p><span class="s1">x = -4</span></p> <p><span class="s1"></span> </p> <p><span class="s1">(b) 9 - 6(x+1) = 2(x-4) + 27</span></p> <p><span class="s1">9 - 6x - 6 = 2x - 8 + 27</span></p> <p><span class="s1">3 - 6x = 2x + 19</span></p> <p><span class="s1">8x = 3-19</span></p> <p><span class="s1">x = (-16)/8</span></p> <p><span class="s1">x = -2</span></p> <p><span class="s1"></span> </p> <p><span class="s1">Fluency</span></p> <p><span class="s1">1.</span></p> <p><span class="s1">a. 7x - 15 = 1</span></p> <p><span class="s1">7x = 16</span></p> <p><span class="s1">x = 16/7 = 2.28</span></p> <p><span class="s1"></span> </p> <p><span class="s1">b. (x+2)/4 = -2</span></p> <p><span class="s1">x+2 = -8</span></p> <p><span class="s1">x = -10</span></p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1">c. (-3/5)x + 2 = 7</span></p> <p><span class="s1">(-3/5)x = 5</span></p> <p><span class="s1">x = -8.333 OR -8 and 1/3</span></p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1">2.</span></p> <p><span class="s1">a. </span><span class="s2">5(x+1) + 4</span><span class="s1"> = 4</span></p> <p><span class="s1"><span class="Apple-tab-span"> </span>6</span></p> <p><span class="s1">5(x+1) + 4 = 24</span></p> <p><span class="s1">5x + 9 = 24</span></p> <p><span class="s1">5x = 15</span></p> <p><span class="s1">x = 3</span></p> <p><span class="s1"></span> </p> <p><span class="s1">b. </span><span class="s2">5(x-3)</span><span class="s1"> + 2 = 7</span></p> <p><span class="s1"><span class="Apple-converted-space"> </span>8</span></p> <p><span class="s1">5(x-3) + 16 = 56</span></p> <p><span class="s1">5x - 15 + 16 = 56</span></p> <p><span class="s1">5x + 1 = 56</span></p> <p><span class="s1">5x = 55</span></p> <p><span class="s1">x = 11</span></p> <p><span class="s1"></span> </p> <p><span class="s1">c. -(3/2)x + 2 = -4</span></p> <p><span class="s1">-(3/2)x = -6</span></p> <p><span class="s1">(3/2)x = 6</span></p> <p><span class="s1">x = 4</span></p> <p><span class="s1"></span> </p> <p><span class="s1">d. 5(x+1) - 2x = 2(3+x)</span></p> <p><span class="s1">5x + 5 - 2x = 6 + 2x</span></p> <p><span class="s1">x = 6 - 5</span></p> <p><span class="s1">x = 1</span></p> <p><span class="s1"></span> </p> <p><span class="s1">e. 3(x-4) - 2(3x+4) = 4(3-x) + 5x + 4</span></p> <p><span class="s1">3x - 12 - 6x - 8 = 12 - 4x + 5x + 4</span></p> <p><span class="s1">3x - 6x + 4x - 5x = 12 + 8 + 12 + 4</span></p> <p><span class="s1">-4x = 36</span></p> <p><span class="s1">x = -9</span></p> <p><span class="s1"></span> </p> <p><span class="s1">f. (1/2) (2- 6 x) - 4 ( x + (3/2)) = -(x-3) + 4</span></p> <p><span class="s1">(2-6x) - 8 (x+ (3/2)) = -2(x-3) + 8</span></p> <p><span class="s1">2-6x - 8x - 12 = -2x + 6 + 8</span></p> <p><span class="s1">12x = 2-12 + 6 + 8</span></p> <p><span class="s1">12x = 4</span></p> <p><span class="s1">x = 1/3</span></p> <p><span class="s1"></span> </p> <p><span class="s1">Applications</span></p> <p><span class="s1">3. a. Let equation equal target number of tiles (150)</span></p> <p><span class="s1">12b + 38 = 150</span></p> <p><span class="s1">12b = 150 - 38</span></p> <p><span class="s1">b = (150-38)/12<span class="Apple-converted-space"></span></span></p> <p><span class="s1">b = 9.33 -> Round up to b = 10</span></p> <p><span class="s1">We need to round up our answer because the supplier does not sell bundles smaller than one full bundle. Hence, 10 is the minimum number we can buy. We will thus be left with 158 tiles.</span></p> <p><span class="s1"></span> </p> <p><span class="s1">b. After buying 10 bundles and selling 150 tiles, the tile warehouse store will be left with x = 158 - 150 = 8 tiles. If the store wants to keep 30 tiles in stock at all times, it has to buy 3 more bundles of tiles. This will allow it to have 30+ 8 = 38 tiles, which exceeds the minimum required stock of 30 tiles.</span></p> <p><span class="s1"></span> </p> <p><span class="s1">Reasoning</span></p> <p><span class="s1">4. Erroneous solution:</span></p> <p><span class="s2">-2(x-3)</span><span class="s1"> = 4</span></p> <p><span class="s1"><span class="Apple-converted-space"> </span>5</span></p> <p><span class="s1"></span> </p> <p><span class="s1">5 . </span><span class="s2">-2(x-3)</span><span class="s1"> = 4 . 5</span></p> <p><span class="s1"><span class="Apple-converted-space"> </span>5</span></p> <p><span class="s1"></span> </p> <p><span class="s1">-2(x-3) = 20</span></p> <p><span class="s1"><b>-2x -<span class="Apple-converted-space"> </span>6 = 20<span class="Apple-tab-span"> </span><span class="Apple-tab-span"> </span><span class="Apple-tab-span"> </span>ERROR: should be -2x + 6 = 20</b></span></p> <p><span class="s1">-2x - 6 + 6 = 20 + 6</span></p> <ul> <li><span class="s3"></span><span class="s1">2x = 26</span></li> </ul> <p><span class="s1">x = -13</span></p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1">Corrected solution:</span></p> <p><span class="s2">-2(x-3)</span><span class="s1"> = 4</span></p> <p><span class="s1"><span class="Apple-converted-space"> </span>5</span></p> <p><span class="s1"></span> </p> <p><span class="s1">5 . </span><span class="s2">-2(x-3)</span><span class="s1"> = 4 . 5</span></p> <p><span class="s1"><span class="Apple-converted-space"> </span>5</span></p> <p><span class="s1"></span> </p> <p><span class="s1">-2(x-3) = 20</span></p> <p><span class="s1">-2x +<span class="Apple-converted-space"> </span>6 = 20</span></p> <p><span class="s1">-2x<span class="Apple-converted-space"> </span>= 20 - 6</span></p> <ul> <li><span class="s3"></span><span class="s1">2x = 14</span></li> </ul> <p><span class="s1">x = - 7<span class="Apple-converted-space"></span></span></p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1">204CCAlg1U2L5LinearWordProblems</span></p> <p><span class="s1">LINEAR WORD PROBLEMS COMMON CORE ALGEBRA I</span></p> <p><span class="s1"></span> </p> <p><span class="s1">Exercise #1:<span class="Apple-converted-space"></span></span></p> <p><span class="s1">(a)Test a: 1</span></p> <p><span class="s1">1 + 5 = 6 (wrong number)</span></p> <p><span class="s1">Test b: 2<span class="Apple-converted-space"></span></span></p> <p><span class="s1">2 + 5 = 7 (wrong number)</span></p> <p><span class="s1">Test c: 8</span></p> <p><span class="s1">8 + 5 = 13 (wrong number)</span></p> <p><span class="s1"></span> </p> <p><span class="s1">(b):Let the number of interest be x</span></p> <p><span class="s1">x + 5 = 17</span></p> <p><span class="s1">x = 17 - 5 = 12</span></p> <p><span class="s1">The number is 12.</span></p> <p><span class="s1"></span> </p> <p><span class="s1">Exercise #2:</span></p> <p><span class="s1">(1) 2n - n + 5 = 3</span></p> <p><span class="s1">(2) n - (2n + 5) = 3</span></p> <p><span class="s1">(3) n + 5 - 2n = 3</span></p> <p><span class="s1">(4) 2n - (n+5) = 3</span></p> <p><span class="s1"></span> </p> <p><span class="s1">The option (4) could be used the find the value of the number, n, because its first term (2n) and its second term (n+5) correspond to those of twice the number and a number that is five more than it is. Furthermore, the equation takes the difference between the two.</span></p> <p><span class="s1"></span> </p> <p><span class="s1">As proof:</span></p> <p><span class="s1">2n - (n+5) = 3</span></p> <p><span class="s1">n - 5 = 3</span></p> <p><span class="s1">n = 8</span></p> <p><span class="s1"></span> </p> <p><span class="s1">The number is 8.</span></p> <p><span class="s1"></span> </p> <p><span class="s1">Exercise #3</span></p> <p><span class="s1">(a) Test 1: Let us say Evie’s age is 5.</span></p> <p><span class="s1">Now: Evie’s father is 36 + 5 = 41</span></p> <p><span class="s1">3 years from now: Evie’s father should be 44, but five times her age (8) is 40.<span class="Apple-converted-space"></span></span></p> <p><span class="s1">This number is wrong.</span></p> <p><span class="s1"></span></p> <p><span class="s1">Test 2: Let us say Evie’s age is 10.</span></p> <p><span class="s1">Now: Evie’s father is 36 + 10 = 46</span></p> <p><span class="s1">3 years from now: Evie’s father should be 49, but five times her age (10) is 50.<span class="XXXXX-converted-space"></span></span></p> <p><span XXXXX="s1">XXXX number is wrong.</span></p> <p><span class="XX"></span></p> <p><span XXXXX="s1">(b) Let Evie’s age now be x, and her XXXXXX’s age XX current XXXX be x + XX.</span></p> <p><span XXXXX="s1">XXX XXXX’s age three XXXXX XXXX XXX XX x + X, and her father’s age 3 XXXXX from XXX XX 5x + 15, or also, x + XX + 3 = x + XX</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">Three XXXXX from now: her XXXXXX’s age is equal to:</span></p> <p><span XXXXX="s1">XX + 15 = x + 39</span></p> <p><span XXXXX="XX">4x = 24</span></p> <p><span class="XX">x = X</span></p> <p><span class="XX">XXXXX, Evie XX 6 XXXXX old XXX.</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">XXXXXXXX #X</span></p> <p><span class="s1">XXXX = x, XXX = y</span></p> <p><span class="s1">XXXXXXXX 1: <span class="XXXXX-tab-span"> </span><span XXXXX="Apple-tab-span"> </span>x + 12 = y</span></p> <p><span XXXXX="s1">EQUATION X: <span class="XXXXX-tab-span"> </span><span class="Apple-tab-span"> </span>(X/2) y = x - X</span></p> <p><span class="s1">XXX EQUATION 2 be transformed XXXX XXXXXXXX 3 (multiply both sides by 2): y = 2x - 4</span></p> <p><span class="s1">XXXXXXXXX, XXXXXXXX XXXXXXXX X XXX EQUATION X:</span></p> <p><span class="XX">x + XX = 2x - X</span></p> <p><span XXXXX="s1">x = XX</span></p> <p><span class="XX">y = x + XX = XX + XX = XX</span></p> <p><span class="XX">XXXX XXX 16 XXXXXXX, Jim has 28 XXXXXXX</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">FLUENCY</span></p> <p><span XXXXX="s1">X. (1) The first equation, XX + (4n -2) = XX , could be XXXX to XXXX the value of XXX number n. XXXX XX because XXX XXXXX XXXXXXXX contains XXX XXX of three XXXXX a XXXXXX XXX 2 less XXXX 4 times that same number, and XXXXX XXXXX sum XXX XXXXXXX it to the target number XX 15.</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">2.</span></p> <ol> <li><span class="XX">Let the sum XX X less than 5 times a XXXXXX and XXX XXXXXX XXXXXXXXX XX X XXXXXXXXX 24 XX:</span></li> </ol> <p><span class="XX">5x - 3 + (x+X) = XX</span></p> <p><span XXXXX="s1">XXXXXXX the equation:</span></p> <p><span XXXXX="s1">6x + 6 = XX</span></p> <p><span class="s1">x = XX/6 = 3</span></p> <p><span class="s1"></span> </p> <p><span class="s1">(b) XXX XXX’s age be t, Andrew’s age XX a, Sara’s age XX s. The XXXXXXXXX XXX XX XXXXXXX:</span></p> <p><span class="s1">t =<span class="Apple-XXXXXXXXX-XXXXX"> </span>2a + 4</span></p> <p><span class="XX">s = 5a - X<span XXXXX="Apple-XXXXXXXXX-space"></span></span></p> <p><span XXXXX="XX">t = s because Tom XXX Sara XXX XXXXX.</span></p> <p><span XXXXX="s1">2a + X = 5a - X</span></p> <p><span XXXXX="XX">3a = 12</span></p> <p><span class="s1">a = X</span></p> <p><span class="s1">t= 2(4) + 4 = 12</span></p> <p><span class="XX">s = XX - X = XX<span class="XXXXX-XXXXXXXXX-XXXXX"> </span></span></p> <p><span class="XX">XXXXXX XX X XXXXX XXX.<span class="XXXXX-converted-space"></span></span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">(c) XXXXX months XX use = x, x=1 XXX XXXX XX plan XX XXXXX by $35(x) + $12.XX = $XX.XX, XXX total XXXXX XXX 450, XXXX per XXXX XX XX.X/XXX = $0.XXX.</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">(d)<span class="Apple-XXXXXXXXX-space"> </span>Daniel’s son’s age is x, Daniel’s age is x + 26. XX six years, XXXXXX ’s XXX XXXX XX x+6, Daniel XXXX XX X(x+X) or x + 26 + 6 = x + XX.</span></p> <p><span class="XX"></span> </p> <p><span class="s1">Hence, XXX XXXXXX’s age in 6 XXXXX be either 3(x+X) or x + 32.</span></p> <p><span XXXXX="s1">Equating both XXXXXXXXXXXXX XXX Daniel’s age in X XXXXX, XX XXX:</span></p> <p><span class="s1">X(x+6) = x + 32</span></p> <p><span class="XX">XX + 18 = x + 32</span></p> <p><span XXXXX="s1">XX - x = XX</span></p> <p><span class="XX">2x = 14</span></p> <p><span XXXXX="XX">XXXXXX’s XXX’s present age: x = X XXXXXX’s XXXXXXX age: x + 26 = XX</span></p> <p><span class="s1"></span> </p> <p><span class="XX">Presently, Daniel’s son XX X XXX XXXXXX XX XX.<span XXXXX="XXXXX-converted-space"></span></span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">XXXXXXXXXXXX</span></p> <p><span class="s1">X. Let age XX XXXXXXX XX x, XXXX be 2(x-10), XXXXX be XX - 12, Matt be 0.XX + 6</span></p> <p><span class="s1">The XXXXX of XXXXX ages is given by XXX XXXXXXXX:</span></p> <p><span XXXXX="XX">x + X(x - XX) + 2x - 12 + 0.5x + 6 = 106</span></p> <p><span class="s1">x + 2x - 20 + XX - XX + X.5x + X = XXX</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">X.5x = XXX</span></p> <p><span XXXXX="s1">x = 24 (Therefore, XXXXXXX is XX)</span></p> <p><span class="s1">XXXX XX 2(XX-10) = 28 XXXXX old.</span></p> <p><span XXXXX="XX">Brian XX 2(24) - XX = XX XXXXX XXX.</span></p> <p><span class="XX">Matt is X.X(24) + 6 = XX years old.</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">Reasoning</span></p> <p><span XXXXX="XX">Let 0.15x+25 = 0.10x + 18.5</span></p> <p><span class="s1">0.XXX = -X.X</span></p> <p><span class="s1">x = -XXX</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">XXXXX 130 XXXXXXX, the two plans XXXX XXXXXX the XXXX XXXXXX.</span></p> <p><span class="s1"></span> </p> <p><span class="s1">XXXX means XXXX Tanisha’s plan is XXXXXXXXX more expensive than Rebecca’s plan.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="XX"></span> </p> <p><span class="XX"></span> </p> <p><span class="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">428CCAlg1U2L2SeeingStructuretoSolveEquations<span XXXXX="XXXXX-converted-space"></span></span></p> <p><span class="s1">XXXXXX XXXXXXXXX XX XXXXX XXXXXXXXX XXXXXX CORE XXXXXXX I</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">XXXXXXXX #1</span></p> <ol> <li><span XXXXX="s1">x XXX multiplied XX 5 XXX increased XX 3, XXX then XXX entire XXXX XXXX XXXX of the equation was XXXXXXX to 23.</span></li> <li><span class="s1"> XX + X = 23</span></li> </ol> <p><span class="XX">5x = 23 - 3</span></p> <p><span XXXXX="s1">5x = 20</span></p> <p><span class="s1">x = X</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">Exercise #X</span></p> <p><span class="XX">(a) What happened XX x? x was reduced by X, divided by X and X was XXXXX to XXX XXXXXX XXX. It XXX then XXXXXXX XX -6.<span XXXXX="Apple-XXXXXXXXX-XXXXX"></span></span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">x - X</span><span XXXXX="s1"> + 7 = 23</span></p> <p><span class="s1"><span class="XXXXX-converted-XXXXX"> </span>X</span></p> <p><span class="XX"></span> </p> <p><span class="XX">x - 3 + 14 = 46</span></p> <p><span XXXXX="XX">x = XX - 14 + 3</span></p> <p><span XXXXX="s1">x = XX</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">(b) What XXXXXXXX to x? x XXX XXXXXXXXX XX 1, x+X was multiplied XX X, XXX the whole XXX XXX XXXXXXX by 2. It was XXXX equated XX -X.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">4(x+1) - 2 = -X</span></p> <p><span class="XX">4x + X - X = -6</span></p> <p><span XXXXX="XX">4x = -6 + 2 - 4</span></p> <p><span XXXXX="s1">XX = -X</span></p> <p><span class="s1">x = -2</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">XXXXXXXX #X</span></p> <p><span class="s1">(a) -2 (x - 4) + 8 = 2</span></p> <p><span XXXXX="XX"><span class="XXXXX-tab-span"> </span>-X(x-4) + X = X</span></p> <p><span XXXXX="s1"><span class="XXXXX-tab-span"> </span>-2 (x-4) = -X</span></p> <p><span class="s1"><span XXXXX="XXXXX-tab-span"> </span>(x-4) = X</span></p> <p><span class="s1"><span XXXXX="XXXXX-tab-span"> </span>x = 4+3</span></p> <p><span XXXXX="s1"><span XXXXX="Apple-tab-span"> </span>x = X</span></p> <p><span XXXXX="s1">(b) Distributive property</span></p> <p><span XXXXX="XX">-2 (x - 4) + X = X</span></p> <p><span XXXXX="XX"><span class="Apple-tab-span"> </span>-2x + 8 + 8 = X</span></p> <p><span class="s1"><span XXXXX="XXXXX-tab-span"> </span>-2x = -XX</span></p> <p><span XXXXX="XX"><span XXXXX="XXXXX-tab-span"> </span>x = -14/-2</span></p> <p><span class="s1"><span class="Apple-tab-span"> </span>x = 7</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">Exercise #X</span></p> <p><span class="XX">(a) Setting up the equation: 5x - XX = 35</span></p> <p><span class="s1"><span class="XXXXX-tab-span"> </span>XX = XX</span></p> <p><span XXXXX="XX"><span class="XXXXX-tab-span"> </span>x = 9</span></p> <p><span class="XX">XXXXXXXXXXXX x = X into the XXXXXXXX equation</span></p> <p><span class="s1">5 (9) - 10 = 35</span></p> <p><span XXXXX="XX" <the="" XXXXXXXX="" XXXXX,="" so="" XXX="" XXXXXX="" is="" correct.="">span class="XXXXX-XXXXXXXXX-space"&XX;</span></p> <p><span XXXXX="s1">(b) XXXXXXX up the equation: (X(x+X)) + 10 = X</span></p> <p><span class="XX">Using XXX distribution XXXXXX:</span></p> <p><span XXXXX="XX">XX + 21 + 10 = 4</span></p> <p><span class="XX">XX = 4- 21 - 10</span></p> <p><span XXXXX="s1">XX = - 27</span></p> <p><span XXXXX="XX">x = -X</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">Fluency</span></p> <p><span class="XX">X. x/5 - 3 is comprised of x XXXXXXX XX X, XXX reduced (subtracted) by 3.</span></p> <p><span class="s1">Hence, the correct XXXXXX XX (3).</span></p> <p><span class="s1"></span> </p> <p><span class="s1">X. 6x + X = X</span></p> <p><span XXXXX="XX">6x = X - X</span></p> <p><span XXXXX="s1">6x = 3</span></p> <p><span XXXXX="s1">x = 3/6 = X/2</span></p> <p><span class="XX">XXX answer is (2)</span></p> <p><span class="s1"></span> </p> <p><span class="s1">X. 5(x-X) - X = 24</span></p> <p><span XXXXX="XX">X(x-X) = 24 + X</span></p> <p><span class="XX">5x - 10 = XX</span></p> <p><span XXXXX="s1">5x = 40</span></p> <p><span class="XX">x = XX/X = 8</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">The correct XXXXXX XX (X)</span></p> <p><span class="s1"></span> </p> <p><span class="XX"><b>Applications</b></span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">4.<span class="Apple-XXXXXXXXX-XXXXX"></span></span></p> <p><span XXXXX="XX">(x + 5) </span><span class="XX">= X</span></p> <p><span XXXXX="s1"><span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>3</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">x + X = 21</span></p> <p><span class="XX">x = XX - 5</span></p> <p><span XXXXX="XX">x = 16</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">X. XX the present, XXX Max’s age be m, Zeke’s age be z. <span class="Apple-XXXXXXXXX-XXXXX"></span></span></p> <p><span XXXXX="XX">Let us set up XXX equation.</span></p> <p><span XXXXX="XX">2(m-X) + X = 26<span XXXXX="XXXXX-converted-space"></span></span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">X = X</span></p> <p><span class="s1">Substituting z = X</span></p> <p><span XXXXX="XX">2 (m - X) + 8 = XX</span></p> <p><span XXXXX="XX">XX - X + 8 = XX</span></p> <p><span class="s1">XX = XX + 6 - X</span></p> <p><span class="XX">2m = 24</span></p> <p><span XXXXX="XX">m = XX</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">XXX XXXXXX XX XXXXXXX because m - 3 = 9, to double it is 18, and XX add it to X XX 26.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">The XXXXXXXX holds.</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">X.<span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>(a) F = XX + 2L</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">(b) X = 2W + XX</span></p> <p><span XXXXX="XX">F = 2(12) + 2(XX)</span></p> <p><span XXXXX="s1">F = XX</span></p> <p><span class="XX"></span> </p> <p><span class="s1">(c) XX F = XXX, XXX L = 30, then:</span></p> <p><span class="XX">120 = XX + X(XX)</span></p> <p><span class="XX">2W = XX</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">X. (a) x was XXXXXXXXXX by X, XXX result was XXXXXXX by 1, the result was multiplied XX 5, the XXXXXX was divided by X, XXX result was reduced XX X, XXX XXXXXX was equated XX XX.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">(b) </span><span XXXXX="s2">X (XX - 1) </span><span class="XX">- X = XX</span></p> <p><span class="XX"><span XXXXX="XXXXX-tab-span"> </span>3</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">Multiply XXXXXXXXXX by X, XXXXXX XXXX hand XXXX of XXX XXXXXXXX</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">10x - 5 - XX = XX</span></p> <p><span class="XX">XXX = 50</span></p> <p><span class="s1">x = 50/XX</span></p> <p><span class="s1">x = 5</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">8. (a) x XXX XXXXXXXXXX by 3, XXX XXXXXX was added to X, the XXXXXX XXX XXXXXXXXXX by X, XXX XXXXXX XXX equated XX -16.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">X(XX + 2) = -XX</span></p> <p><span class="s1">3x + X = -XX</span></p> <p><span class="XX">3x = -XX</span></p> <p><span class="s1">x = -XX</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">(b) X(XX + X) = -XX</span></p> <p><span class="s1">12x + 8 = -16</span></p> <p><span class="XX">XXX = -24</span></p> <p><span class="s1">x = -2</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">464CCAlg1U2L8Inequalities<span class="Apple-XXXXXXXXX-space"></span></span></p> <p><span class="XX">XXXXXXXXXXXX (XXXX ANOTHER TRUE/FALSE XXXXXXXX) XXXXXX CORE ALGEBRA I</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">Exercise #1</span></p> <ol> <li><span class="XX">XXXX (b) True (c) XXXXX (d) True (e) True (f) True (g) XXXXX (h) True</span></li> </ol> <p><span XXXXX="XX"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">Exercise #2</span></p> <p><span class="s1" <XXX="" statement="" XX="" XXXX.="" 4="" 12="" more="" than="" -8="" (a="" positive="" number="" always="" a="" negative="" number).="">span XXXXX="Apple-XXXXXXXXX-XXXXX"&XX;</span></p> <p><span XXXXX="XX"></span> </p> <ol> <li><span XXXXX="XX">XXXX</span></li> </ol> <p><span class="XX"></span> </p> <p><span XXXXX="XX">-4<span XXXXX="Apple-tab-span"> </span>-3<span class="XXXXX-tab-span"> </span>-X<span class="Apple-tab-span"> </span>-1<span XXXXX="Apple-tab-span"> </span>X<span class="Apple-tab-span"> </span>X<span XXXXX="Apple-tab-span"> </span>X<span XXXXX="Apple-tab-span"> </span>3</span></p> <p><span class="XX">XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">(b) False</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">-X <span XXXXX="Apple-tab-span"> </span>-4<span XXXXX="Apple-tab-span"> </span>-X</span></p> <p><span class="s1">_______________</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">(c) XXXX</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">-6<span XXXXX="Apple-tab-span"> </span>-5<span XXXXX="XXXXX-tab-span"> </span>-X<span XXXXX="XXXXX-tab-span"> </span>-3<span class="XXXXX-tab-span"> </span>-2<span class="Apple-tab-span"> </span>-1<span XXXXX="XXXXX-tab-span"> </span>0</span></p> <p><span class="XX">________________________________________</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX">Exercise #X</span></p> <p><span class="s1">X(x - X) ≥ 2x + X</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">(a) 3(XX - X) ≥ 2 (XX) + X</span></p> <p><span class="XX">XX ≥ 20 + 1</span></p> <p><span class="s1">XX ≥ 21</span></p> <p><span class="XX">The XXXXXXXXXX XX false</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">(b) X(X - 2) ≥ X (X) + 1</span></p> <p><span class="XX">9 ≥ XX</span></p> <p><span XXXXX="s1">XXX XXXXXXXXXX XX XXXXX</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">(c) 3(1 - 2) ≥ 2 (X) + X</span></p> <p><span class="s1">-X ≥ X</span></p> <p><span XXXXX="XX">The inequality XX false</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">(d) 3(X - X) ≥ X (7) + X</span></p> <p><span class="s1">XX ≥ XX</span></p> <p><span XXXXX="s1">XXX inequality is true</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">Exercise #X</span></p> <p><span class="s1">(a) XX + 4 &XX; 4x - X</span></p> <p><span class="s1">x = X</span></p> <p><span class="XX">X(1) + X > 4(1) - X</span></p> <p><span XXXXX="XX">6 > 3</span></p> <p><span class="XX">The inequality is XXXX</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">(b) -3 (x+X) ≥ </span><span XXXXX="s2">x+7</span></p> <p><span XXXXX="s1"><span class="XXXXX-tab-span"> </span><span XXXXX="XXXXX-tab-span"> </span>2<span class="XXXXX-tab-span"> </span><span XXXXX="Apple-tab-span"> </span>for x = -X</span></p> <p><span XXXXX="XX">-6 (x + 5) ≥ x + 7</span></p> <p><span XXXXX="s1">-X (-3 + X) ≥ -3 + X</span></p> <p><span XXXXX="s1">-XX ≥ X</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">XXX inequality is XXXXX</span></p> <p><span class="s1"></span> </p> <p><span class="XX">(c) x</span><span class="s4"><XXX>2 </XXX></span><span class="s1">-10x + X &XX; 20 + XX<span XXXXX="XXXXX-tab-span"> </span>XXX x = -2</span></p> <p><span XXXXX="s1">Substitute x = -X</span></p> <p><span class="XX">(-2)</span><span class="s4"><sup>X </sup></span><span XXXXX="s1">-XX(-2) + X &XX; 20 + 5(-X)</span></p> <p><span class="s1">4 + 20 + X < XX - 10</span></p> <p><span class="s1">XX < XX</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">The XXXXXXXXXX XX false</span></p> <p><span class="s1"></span> </p> <p><span class="XX">(d) </span><span XXXXX="s2">X (x - 5)</span><span XXXXX="s1"> + X ≤ </span><span class="s2">x - X </span><span XXXXX="XX"><span XXXXX="Apple-converted-XXXXX"> <span class="Apple-tab-span"> </span></span>for x = X</span></p> <p><span class="s1"><span XXXXX="Apple-tab-span"> </span>X<span XXXXX="XXXXX-tab-span"> </span><span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>X</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"> </span><span XXXXX="s2">2 (5 - 5)</span><span XXXXX="s1"> + 1 ≤ </span><span XXXXX="XX">X - 2 </span><span class="s1"><span class="XXXXX-converted-XXXXX"> <span class="XXXXX-tab-span"> </span></span>for x = 5</span></p> <p><span class="s1"><span XXXXX="Apple-tab-span"> </span>3<span XXXXX="XXXXX-tab-span"> </span><span class="Apple-converted-XXXXX"> </span>9</span></p> <p><span class="s1"></span> </p> <p><span class="XX"><span class="Apple-tab-span"> </span>X + X ≤ 1/X</span></p> <p><span XXXXX="XX"><span class="XXXXX-tab-span"> </span><span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>1 ≤ 1/3</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1" <XXX="" inequality="" is="" false="">span class="Apple-XXXXXXXXX-XXXXX"></span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">INEQUALITIES COMMON CORE XXXXXXX I XXXXXXXX</span></p> <p><span XXXXX="s1">XXXXXXX</span></p> <ol> <li><span XXXXX="XX">(a) XXXX (b) XXXXX (c) False (d) XXXX (e) XXXXX (f) True (g)True (h) False</span></li> </ol> <p><span class="XX">2. (a) 3x + 2 ≤ 2x - X <span class="XXXXX-tab-span"> </span>for x = X</span></p> <p><span XXXXX="XX"><span class="Apple-tab-span"> </span>3(X) + 2 ≤ X(8) - 5</span></p> <p><span class="s1"><span class="XXXXX-tab-span"> </span>24 + 2 ≤ 16 - X</span></p> <p><span class="s1"><span XXXXX="Apple-tab-span"> </span>26 ≤ XX</span></p> <p><span class="s1">XXX inequality XX false</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">(b)<span class="Apple-converted-XXXXX"> </span>XX + X ≤ X - 3x <span class="Apple-tab-span"> </span>XXX x = -2</span></p> <p><span XXXXX="XX"><span class="Apple-XXXXXXXXX-XXXXX"> </span>X(-2) + X ≤ X - X(-2)</span></p> <p><span XXXXX="s1"><span XXXXX="XXXXX-converted-XXXXX"> </span>-X + 2 ≤ -X</span></p> <p><span XXXXX="s1">The inequality XX XXXX</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">(c) (x-X)</span><span XXXXX="s4"><XXX>2 </XXX></span><span XXXXX="XX">&XX; -X(x+X)<span class="XXXXX-tab-span"> </span>for x = X</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">(X-3)</span><span class="s4"><XXX>X </XXX></span><span class="s1">> -X(3+X)</span></p> <p><span XXXXX="XX">X &XX; -XX</span></p> <p><span class="s1">XXX inequality is true</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">(d) </span><span XXXXX="s2">X (3-XX)</span><span XXXXX="s1"> ≤ 2x - X(x+1)<span XXXXX="XXXXX-tab-span"> </span>for x = -1</span></p> <p><span XXXXX="s1"><span class="Apple-tab-span"> </span>5</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s2">X (3+X)</span><span class="s1"> ≤ -2 - X(X)<span class="XXXXX-tab-span"> </span>XXX x = -X</span></p> <p><span XXXXX="s1"><span XXXXX="Apple-converted-XXXXX"> </span>5</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">XX/5 ≤ -2</span></p> <p><span XXXXX="XX">XXX XXXXXXXXXX XX false</span></p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1">(e) </span><span XXXXX="s2">3</span><span XXXXX="XX"><XXX>2</XXX></span><span class="s2"> - 4(3) + X</span><span XXXXX="XX"> &XX; </span><span class="s2">3(3) + X</span></p> <p><span XXXXX="s1"><span XXXXX="XXXXX-tab-span"> </span>X<span XXXXX="Apple-tab-span"> </span><span class="XXXXX-XXXXXXXXX-XXXXX"> </span>X<span XXXXX="Apple-tab-span"> </span><span class="XXXXX-tab-span"> </span><span XXXXX="XXXXX-tab-span"> </span>for x = X</span></p> <p><span class="s1"></span> </p> <p><span class="s2">X - XX + X</span><span XXXXX="XX"> &XX; X</span><span class="s2"> + 1</span></p> <p><span XXXXX="s1"><span class="XXXXX-XXXXXXXXX-XXXXX"> </span>X<span XXXXX="Apple-tab-span"> </span><span class="XXXXX-converted-space"> </span>X<span XXXXX="XXXXX-tab-span"> </span><span XXXXX="Apple-tab-span"> </span><span class="Apple-tab-span"> </span>XXX x = X</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s2">6</span><span XXXXX="s1"> &XX; </span><span XXXXX="XX">XX</span></p> <p><span XXXXX="XX">6 <span XXXXX="Apple-converted-XXXXX"> </span>X<span class="Apple-tab-span"> </span><span class="Apple-tab-span"> </span><span class="XXXXX-tab-span"> </span>for x = X</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">1 > 2 for x = 3</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">The XXXXXXXXXX is false</span></p> <p><span class="s1"></span> </p> <p><span class="s1">| </span><span XXXXX="XX">-X (5 - x) </span><span XXXXX="s1">| ≥ </span><span class="XX">XX - X</span></p> <p><span XXXXX="XX"><span XXXXX="Apple-converted-space"> </span>3<span class="Apple-tab-span"> </span><span class="XXXXX-tab-span"> </span>2<span XXXXX="Apple-tab-span"> </span><span class="XXXXX-tab-span"> </span>XXX x = -X</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">| </span><span class="s2">-2 (5 +1) </span><span XXXXX="s1">| ≥ </span><span XXXXX="XX">-3 - 1</span></p> <p><span class="XX"><span class="XXXXX-XXXXXXXXX-space"> </span>X<span class="XXXXX-tab-span"> </span><span class="XXXXX-tab-span"> </span>2<span XXXXX="XXXXX-tab-span"> </span><span XXXXX="Apple-tab-span"> </span>for x = -X</span></p> <p><span class="XX"></span> </p> <p><span class="XX">4 ≥ -X</span></p> <p><span XXXXX="s1">The inequality XX true</span></p> <p><span class="s1"></span> </p> <p><span class="s1"><b>Applications<span class="Apple-converted-XXXXX"></span></b></span></p> <p><span class="XX"><b>X.<span XXXXX="Apple-XXXXXXXXX-XXXXX"></span></b></span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"><b>x = XX</b></span></p> <p><span XXXXX="XX">X(x + X) - 1</span><span XXXXX="s1"> + X (2x - 3)<span class="Apple-XXXXXXXXX-XXXXX"> </span>≤ XXX</span></p> <p><span XXXXX="XX"><span XXXXX="Apple-converted-space"> </span>X</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">X(XX + 5) - X</span><span XXXXX="s1"> + 4 (2(XX) - X)<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>≤ 125</span></p> <p><span class="s1"><span XXXXX="XXXXX-XXXXXXXXX-space"> </span>X</span></p> <p><span class="XX"></span> </p> <p><span class="s1">50/X + XX ≤ XXX</span></p> <p><span XXXXX="XX">109 ≤ 125</span></p> <p><span class="s1"></span> </p> <p><span class="s1">XXX inequality XX true. XXX XXXXXXX XX safe XX run XX XXXXXXXX = XX</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"><b>x = XX</b></span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">3(x + 5) - X</span><span XXXXX="s1"> + X (2x - 3)<span XXXXX="Apple-converted-XXXXX"> </span>≤ 125</span></p> <p><span XXXXX="s1"><span class="XXXXX-converted-XXXXX"> </span>X</span></p> <p><span class="s1"></span> </p> <p><span class="XX">X(XX + X) - X</span><span class="XX"> + 4 (X(13) - 3)<span class="Apple-converted-XXXXX"> </span>≤ XXX</span></p> <p><span XXXXX="XX"><span XXXXX="XXXXX-converted-space"> </span>X</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">XX/X + 92 ≤ 125</span></p> <p><span XXXXX="s1">118.X ≤ 125</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">XXX XXXXXXXXXX is XXXX. The XXXXXXX XX XXXX XX XXX at pressure = XX</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"><b>x = XX</b></span></p> <p><span class="s2">3(x + X) - 1</span><span XXXXX="XX"> + X (XX - 3)<span class="Apple-XXXXXXXXX-space"> </span>≤ 125</span></p> <p><span class="XX"><span XXXXX="Apple-converted-XXXXX"> </span>X</span></p> <p><span class="XX"></span> </p> <p><span class="s2">3(14 + X) - X</span><span XXXXX="XX"> + 4 (X(XX) - X)<span class="Apple-XXXXXXXXX-XXXXX"> </span>≤ 125</span></p> <p><span XXXXX="XX"><span XXXXX="Apple-converted-space"> </span>2</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">28 + 100 ≤ 125</span></p> <p><span class="s1">XXX ≤ XXX</span></p> <p><span class="XX">The XXXXXXXXXX XX XXXXX. XXX machine is unsafe XX XXX at pressure = XX</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">(b) x = 5</span></p> <p><span class="XX">X(x + 5) - X</span><span class="XX"> + 4 (2x - X)<span class="Apple-XXXXXXXXX-XXXXX"> </span>> XX</span></p> <p><span XXXXX="XX"><span class="XXXXX-converted-space"> </span>X</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">3(X + X) - 1</span><span XXXXX="s1"> + 4 (2(X) - 3)<span XXXXX="XXXXX-XXXXXXXXX-space"> </span>&XX; XX</span></p> <p><span class="XX"><span class="Apple-converted-XXXXX"> </span>X</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">14.X + XX > 35</span></p> <p><span XXXXX="s1">XX.5 > 35</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX" <XXX="" machine="" XXXX="" run="" as="" XXX="" pressure="" XX="" XXXXX="" 35="" pounds="" per="" XXXXXX="" inch.="">span class="XXXXX-XXXXXXXXX-space"></span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">XXXXXXXXX</span></p> <p><span XXXXX="XX">X. (a) 4(-X) + X &XX; X - 3(-X)</span></p> <p><span XXXXX="XX"><span XXXXX="Apple-tab-span"> </span>-X &XX; 7</span></p> <p><span XXXXX="s1" <XXX="" correct="" sign="" is="" <="">span class="Apple-XXXXXXXXX-XXXXX"&XX;</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">(b) (XX + X)/ (-X) < 4 / (2-3x)</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">(X(-X) + 1)/ (-X) > 4 / (2-X(-X))</span></p> <p><span class="XX">X &XX; 4/X</span></p> <p><span class="s1">1 &XX; X/X</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">XXX XXXXXXX XXXX XX &XX;</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">(c) XX</span><span XXXXX="s4"><XXX>2 </XXX></span><span class="s1">+5 &XX; |X - 9x|</span></p> <p><span XXXXX="s1">2(4)</span><span XXXXX="XX"><sup>X </sup></span><span class="XX">+5 &XX; |1 - X(X)|</span></p> <p><span class="s1">XX &XX; XX</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">XXX correct sign XX ></span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">(d) ((3(XX - 5)) / 3) + 2 <span XXXXX="Apple-tab-span"> </span>< X(3(x) - 6)</span></p> <p><span class="s1">((X(X(5) - X)) / X) + X <span class="Apple-tab-span"> </span>&XX; 8(3(5) - X)</span></p> <p><span XXXXX="XX">7 &XX; 72</span></p> <p><span class="s1"></span> </p> <p><span class="XX">The correct XXXX XX <</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">468CCAlg1U2L1EquationsandTheirSolutions</span></p> <p><span XXXXX="XX">XXXXXXXXX AND THEIR SOLUTIONS XXXXXX XXXX ALGEBRA I</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">Exercise #X</span></p> <p><span class="XX">(X) 2(XX + 1)<span XXXXX="Apple-converted-XXXXX"> </span>is XXX an XXXXXXXX.</span></p> <p><span class="XX">The other three options are XXXXXXXXX as they are in XXX XXXXXXXX XXXXXX.</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">Exercise #2</span></p> <p><span XXXXX="s1">(a) XX XXXXXX XXXXXXXXX XXXXXXX XX - X = 10 - x is XXXX or false as we XX XXX XXXX XXX value XX the unknowns, and hence XX do XXX know XX the equation holds.</span></p> <p><span class="XX"></span> </p> <p><span class="s1">(b) XX x = X, the XXXXXXXX XXXXXXXXX to 10 - 8 = 10 - 5 &XX;&XX;&XX; 2 = X. The equation XXXX be XXXXX.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">(c) 2x - 8 = 10 - x</span></p> <p><span XXXXX="s1">2(6) - 8 = 10 - 6</span></p> <p><span XXXXX="s1">4 = X</span></p> <p><span XXXXX="XX" <the="" equation="" is="" XXXX="" XX="" XXXX="" XXXXX="" XXXX.="">span class="XXXXX-converted-XXXXX"></span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">Exercise #X</span></p> <p><span class="XX">(a)<span XXXXX="XXXXX-converted-space"> </span>XX + X = 17</span></p> <p><span XXXXX="XX">2(7) + X = 17</span></p> <p><span XXXXX="s1">17 = XX</span></p> <p><span XXXXX="s1">XXX XXXXXXXX XX true.</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">(b) </span><span XXXXX="XX">(x - XX)</span><span XXXXX="XX"> = -4</span></p> <p><span class="s1"><span XXXXX="XXXXX-converted-space"> </span>X</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">(XX - XX)</span><span XXXXX="s1"> = -4</span></p> <p><span class="s1"><span XXXXX="Apple-XXXXXXXXX-space"> </span>X</span></p> <p><span class="s1"></span> </p> <p><span class="XX">(-10)</span><span XXXXX="XX"> = -4</span></p> <p><span class="XX"><span XXXXX="Apple-XXXXXXXXX-space"> </span>5</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">-2 = -X</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">XXX XXXXXXXX XX XXXXX</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">(c) 2 (x+X) = 6 (x - X)<span XXXXX="Apple-converted-space"></span></span></p> <p><span class="s1">X (X + X) = 6 ( X - X)</span></p> <p><span class="s1">18 = 18</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">XXX XXXXXXXX is XXXX</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">(d)<span XXXXX="Apple-converted-XXXXX"></span></span></p> <p><span class="s1">x</span><span XXXXX="XX"><XXX>X </sup></span><span XXXXX="s1">-X</span><span XXXXX="s4"> </span><span class="s1">= 2x + 2</span></p> <p><span XXXXX="s1">(-X)</span><span XXXXX="s4"><XXX>2 </sup></span><span XXXXX="XX">-1</span><span XXXXX="s4"> </span><span XXXXX="XX">= X(-X) + X</span></p> <p><span class="s1">1 -1 = X - 2</span></p> <p><span class="XX">0 = 0</span></p> <p><span XXXXX="s1">XXX XXXXXXXX XX true</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">(e) </span><span XXXXX="XX">X (x + 2)</span><span class="s1"> - X = 5</span></p> <p><span class="XX"><span XXXXX="Apple-tab-span"> </span>X</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s2">3 ((X) + X)</span><span XXXXX="XX"> - X = 5</span></p> <p><span class="s1"><span class="Apple-converted-XXXXX"> </span>4</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">12 - 4 = XX</span></p> <p><span class="s1">8 = XX</span></p> <p><span class="XX">The XXXXXXXX is XXXXX</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">(f) X/X x - 1 = -1/X x + X</span></p> <p><span XXXXX="s1">X/4 (X) - X = -1/X (8) + X</span></p> <p><span class="s1">X - X = 9 - 4</span></p> <p><span XXXXX="s1">5 = 5</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">The equation XX true</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">Exercise #4</span></p> <p><span XXXXX="s1">4x - 3 = X x + 11</span></p> <p><span class="s1">X(X) - 3 = X(X) + 11</span></p> <p><span XXXXX="s1">25 = 25</span></p> <p><span class="s1">It XX XXXXXXX as a solution.</span></p> <p><span class="XX"></span> </p> <p><span class="s1">Kirk’s XXXXX XXX to complete XXX operations X-X and X + XX before XXX XXXXXXXXXX 4(X) and X(X).</span></p> <p><span class="s1">XXXXXXXXXXXXXX XXXXXX XXXXXX come XXXXXX addition and subtraction.</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">XXXXXXX</span></p> <p><span class="s1">X. (a) Expression (b) Equation (c) Equation (d) Expression (e) XXXXXXXXXX (f) XXXXXXXX</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">2. (a) x - 4 = XX<span XXXXX="Apple-converted-XXXXX"></span></span></p> <p><span class="s1">8 - X = XX<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"></span></span></p> <p><span XXXXX="XX">X = 12</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">(b) (3+x) / X = X</span></p> <p><span class="s1">(3+X) / 4 = 3</span></p> <p><span class="s1">12/X = 3</span></p> <p><span class="XX">XXX equation XX XXXX. XXX solution XX XXXXX XXX XXX XXXXX XXXXXXXX.</span></p> <p><span class="s1"></span> </p> <p><span class="s1">(c) (x + 2) - 3(x-4) = X</span></p> <p><span XXXXX="s1">(X + X) - 3(4-X) = X</span></p> <p><span class="XX">X - X(0) = X</span></p> <p><span class="XX">6 = X</span></p> <p><span class="s1">The XXXXXXXX XX true. The solution is XXXXX XXX XXX given XXXXXXXX.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">(d) 1/X (x+2) = - 2/X (x-9)</span></p> <p><span class="s1">X/X (X+X) = - X/X (4-9)</span></p> <p><span class="XX">2 = 2</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">The XXXXXXXX is XXXX. The solution is valid for XXX XXXXX equation.</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">XXXXXXXXXXXX</span></p> <p><span XXXXX="s1">3.<span XXXXX="XXXXX-converted-XXXXX"></span></span></p> <p><span XXXXX="XX">XXX X: X = X(1) + X = 11</span></p> <p><span class="XX">XXX X: X = 6(2) + X = 17</span></p> <p><span class="s1">Day 3: X = X(X) + X = 23</span></p> <p><span class="s1">XXX 4: P = X(4) + X = XX</span></p> <p><span class="XX">XXX 5: X = 6(X) + X = 35</span></p> <p><span class="s1">XXX X: P = X(6) + X = XX</span></p> <p><span class="s1">Day X: P = 6(7) + 5 = XX</span></p> <p><span class="XX">XXX X: X = X(8) + 5 = 53</span></p> <p><span class="XX">We will XXXXXXX XXXXX X on Day 1, Stage 2 XX XXX 2 to 3, XXXXX 3 XXX XXX 4 to X, XXX incurable XXXXX XX XXX 8.<span XXXXX="Apple-converted-space"></span></span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">XXXXXXXXX</span></p> <p><span XXXXX="XX">4. XXX + XX = 250</span></p> <p><span XXXXX="XX">(a) Savings XXXXX X XXXXX = XX (9) + 30 = 255</span></p> <p><span XXXXX="s1">Yes, bobby XXXX have XXXXXX XX XXX &XX; 250</span></p> <p><span class="XX">(b) 25w + XX + XXX = 250 + XXX</span></p> <p><span class="s1">XXXXX X XXXXX of XXXXXX = XX(X) + XX + XX(9) = 345</span></p> <p><span class="XX">Bobby needs 250 + XXX = 350</span></p> <p><span class="s1">XXXX weeks is not XXXXXX time XXX Bobby XX XXXX as XXX < 350</span></p> <p><span class="s1"></span> </p> <p><span class="XX"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX">XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX</span></p> <p><span XXXXX="s1">SOLVING XXXXXX INEQUALITIES XXXXXX XXXX ALGEBRA I</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">XXXXXXXX #X</span></p> <p><span class="s1">(a) The XXX XXXXXXXXXX XX X &XX; 11. XXXX XX a true XXXXXXXXXX.</span></p> <p><span XXXXX="s1">(b) XXX XXX XXXXXXXXXX is 0 &XX; X. This is a true inequality.</span></p> <p><span class="s1">(c) The new inequality is 8 &XX; XX. This is a XXXX XXXXXXXXXX.</span></p> <p><span XXXXX="XX">(d) The XXX XXXXXXXXXX is X < 4. XXXX XX a true inequality.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">Exercise #X</span></p> <p><span class="s1">(a) XXX XXX inequality XX -8 < -XX. XXXX is a false inequality.</span></p> <p><span class="XX">(a) The new XXXXXXXXXX XX -X < -X. This XX a false inequality.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">XXXXXXXX #3</span></p> <p><span class="XX">(a) XXX XXXXXXXXXX XX 5 &XX; 8. When XXXXXXXXXX by -4, it XXXXXXX -20 < -32. XXXX XXXXXXX XXXXX.<span class="XXXXX-converted-space"></span></span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">XXXXXXXX #X</span></p> <p><span class="s1">(a) 4x - 3 ≥ 5</span></p> <p><span class="s1">XX ≥ X</span></p> <p><span class="s1">x ≥ 2</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">(b) / (c)</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">The XXXX numbers XXX 3, 4, X, 6, X</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">The XXXXXXXX XX indicated XX the XXXXX &XX;>&XX;&XX;>>&XX;&XX;></span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX"><span XXXXX="Apple-tab-span"> </span><span class="XXXXX-tab-span"> </span><span XXXXX="XXXXX-tab-span"> </span><span XXXXX="XXXXX-tab-span"> </span><span XXXXX="Apple-tab-span"> </span><span class="Apple-tab-span"> </span> <span XXXXX="XXXXX-converted-XXXXX"> </span>>>&XX;&XX;&XX;>&XX;&XX;&XX;&XX;&XX;>>&XX;>>&XX;&XX;>>>&XX;&XX;&XX;>&XX;&XX;>>>&XX;&XX;</span></p> <p><span XXXXX="XX">-10<span class="XXXXX-XXXXXXXXX-space"> </span>-9<span class="Apple-XXXXXXXXX-space"> </span>-8 <span class="XXXXX-XXXXXXXXX-space"> </span>-X<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>-6 <span XXXXX="Apple-converted-XXXXX"> </span>-5 <span class="XXXXX-XXXXXXXXX-XXXXX"> </span>-4<span class="XXXXX-XXXXXXXXX-space"> </span>-X <span XXXXX="XXXXX-converted-XXXXX"> </span>-X <span class="XXXXX-converted-XXXXX"> </span>-X<span class="XXXXX-XXXXXXXXX-space"> </span>0<span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>X <span class="XXXXX-XXXXXXXXX-XXXXX"> </span>2 <span class="Apple-converted-space"> </span>X<span class="XXXXX-XXXXXXXXX-XXXXX"> </span>4<span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>X<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>X<span XXXXX="XXXXX-converted-XXXXX"> </span>7<span class="Apple-converted-space"> </span>8<span class="XXXXX-converted-XXXXX"> </span>9<span class="XXXXX-XXXXXXXXX-XXXXX"> </span>XX</span></p> <p><span class="XX">|XXXX|____|____|XXXX|XXXX|XXXX|____|____|XXXX|____|____|____|XXXX|____|____|XXXX|XXXX|XXXX|____|____|</span></p> <p><span class="XX"></span> </p> <p><span class="XX">Exercise #X<span XXXXX="Apple-converted-space"></span></span></p> <p><span class="s1"></span> </p> <p><span class="s1">(a) Rewrite the left XXXX XXXXXXXXXX XX an equivalent XXXXXXXXXX using XXXXXXXX.</span></p> <p><span class="XX">X - XX &XX; XX</span></p> <p><span class="XX">8 - 16 &XX; XX</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">(b) XXXXX XXX XXXXXXXXXX</span></p> <p><span XXXXX="XX">8 - XX &XX; 16</span></p> <p><span XXXXX="s1">X - 16 &XX; XX</span></p> <p><span class="s1">-8 &XX; XX</span></p> <p><span XXXXX="s1">-4 &XX; x</span></p> <p><span class="XX">x &XX; -X</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">(c) Let x = -6</span></p> <p><span class="s1">XX -X &XX; -4, XXX XXXXXXXX inequality XX true</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">(d)<span class="Apple-XXXXXXXXX-XXXXX"></span></span></p> <p><span XXXXX="s1">XXX XXXXXXXX is indicated XX XXX range >&XX;&XX;&XX;&XX;&XX;&XX;>&XX;</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">&XX;<&XX;<<&XX;<<&XX;<<&XX;&XX;&XX;<<<<<&XX;<&XX;<</span></p> <p><span class="XX">-10<span class="Apple-XXXXXXXXX-XXXXX"> </span>-X<span class="XXXXX-converted-space"> </span>-X <span XXXXX="Apple-converted-space"> </span>-X<span class="Apple-XXXXXXXXX-space"> </span>-6 <span XXXXX="XXXXX-XXXXXXXXX-space"> </span>-5 <span XXXXX="Apple-XXXXXXXXX-space"> </span>-4<span class="XXXXX-converted-XXXXX"> </span>-X <span class="Apple-XXXXXXXXX-XXXXX"> </span>-X <span class="Apple-converted-XXXXX"> </span>-1<span class="Apple-XXXXXXXXX-space"> </span>X<span class="XXXXX-converted-XXXXX"> </span>1 <span class="Apple-XXXXXXXXX-space"> </span>2 <span class="Apple-converted-space"> </span>X<span class="Apple-XXXXXXXXX-XXXXX"> </span>X<span class="XXXXX-converted-space"> </span>5<span class="Apple-XXXXXXXXX-space"> </span>X<span class="Apple-XXXXXXXXX-XXXXX"> </span>7<span class="XXXXX-XXXXXXXXX-space"> </span>8<span class="XXXXX-converted-XXXXX"> </span>X<span XXXXX="XXXXX-XXXXXXXXX-space"> </span>10</span></p> <p><span class="XX">|____|XXXX|XXXX|____|XXXX|____|____|XXXX|____|____|____|____|XXXX|XXXX|XXXX|____|XXXX|XXXX|____|____|</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">XXXXXXXX #6<span class="Apple-converted-space"></span></span></p> <p><span XXXXX="s1">(a)</span></p> <p><span class="XX">8 (x-X) - 3 (XX + X) ≤ 7x + X - X(x+X)</span></p> <p><span class="s1">XX - XX - 6x - X ≤ XX + X - XX - X</span></p> <p><span XXXXX="XX">XX - XX ≤ XX + 1</span></p> <p><span XXXXX="XX">-XX ≤ 20</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">(b)<span XXXXX="Apple-converted-XXXXX"></span></span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">X (x-X) - 3 (XX + 1) ≤ 7x + 4 - X(x+1)</span></p> <p><span XXXXX="XX">8x - XX - XX - 3 ≤ XX + X - XX - 3</span></p> <p><span XXXXX="XX">2x - 19 ≤ 4x + 1</span></p> <p><span XXXXX="XX">-XX ≤ XX</span></p> <p><span XXXXX="XX">-x ≤ 10</span></p> <p><span class="XX">x ≥ -XX</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="XX"><span XXXXX="XXXXX-tab-span"> </span><span XXXXX="Apple-tab-span"> </span><span class="XXXXX-tab-span"> </span> <span class="Apple-XXXXXXXXX-XXXXX"> </span>O>>&XX;>&XX;>&XX;>&XX;&XX;&XX;>&XX;>>&XX;&XX;&XX;>&XX;>>&XX;&XX;&XX;>>>>&XX;</span></p> <p><span XXXXX="XX">-16 -XX -XX- <span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>13 -12<span class="Apple-XXXXXXXXX-XXXXX"> </span>-XX <span XXXXX="XXXXX-converted-XXXXX"> </span>-XX<span class="Apple-converted-XXXXX"> </span>-X<span XXXXX="Apple-XXXXXXXXX-space"> </span>-8 <span XXXXX="XXXXX-converted-space"> </span>-X<span class="Apple-converted-XXXXX"> </span>-6 <span class="XXXXX-XXXXXXXXX-space"> </span>-5 <span class="Apple-converted-space"> </span>-X<span XXXXX="Apple-XXXXXXXXX-space"> </span>-X <span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>-X <span class="Apple-XXXXXXXXX-space"> </span>-1<span class="Apple-XXXXXXXXX-space"> </span>0</span></p> <p><span XXXXX="s1">|____|XXXX|XXXX|____|____|XXXX|____|XXXX|XXXX|____||XXXX|XXXX|____|XXXX|____|XXXX|</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">XXXXXXX</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">(a)<span XXXXX="Apple-converted-space"></span></span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">XX - 6 ≤ 24</span></p> <p><span class="s1">XX ≤ 30</span></p> <p><span class="XX">x ≤ X</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">XXX XXXXXXXX XX indicated XX the range >&XX;&XX;>&XX;&XX;&XX;>&XX;</span></p> <p><span class="s1"></span> </p> <p><span class="XX">&XX;<&XX;<&XX;&XX;&XX;&XX;&XX;&XX;<&XX;<<<&XX;&XX;&XX;&XX;&XX;<&XX;<&XX;&XX;&XX;&XX;<<&XX;&XX;<<&XX;&XX;<<&XX;<&XX;&XX;&XX;<&XX;&XX;&XX;<&XX;&XX;<&XX;&XX;<&XX;&XX;&XX;<<O</span></p> <p><span XXXXX="XX">-XX<span class="Apple-converted-XXXXX"> </span>-9<span XXXXX="Apple-converted-XXXXX"> </span>-8 <span class="Apple-converted-XXXXX"> </span>-X<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>-6 <span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>-5 <span XXXXX="XXXXX-XXXXXXXXX-space"> </span>-4<span class="Apple-converted-space"> </span>-X <span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>-X <span XXXXX="XXXXX-converted-space"> </span>-X<span class="XXXXX-XXXXXXXXX-space"> </span>X<span class="Apple-XXXXXXXXX-XXXXX"> </span>X <span class="Apple-converted-XXXXX"> </span>2 <span XXXXX="Apple-converted-XXXXX"> </span>3<span class="XXXXX-converted-XXXXX"> </span>X<span XXXXX="Apple-converted-space"> </span>5<span class="XXXXX-converted-space"> </span>6<span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>7<span class="Apple-converted-XXXXX"> </span>8<span class="XXXXX-converted-XXXXX"> </span>X<span class="Apple-converted-XXXXX"> </span>10</span></p> <p><span class="XX">|XXXX|____|XXXX|XXXX|XXXX|XXXX|____|XXXX|XXXX|____|____|____|XXXX|XXXX|XXXX|____|XXXX|____|XXXX|____|</span></p> <p><span class="XX"></span> </p> <p><span class="XX">(b)</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">2(5-x) ≤ 12</span></p> <p><span XXXXX="s1">10 - XX ≤ 12</span></p> <p><span class="s1">10 - 12 ≤ 2x</span></p> <p><span class="s1">-X ≤ 2x</span></p> <p><span class="s1">-X ≤ x</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">The XXXXXXXX XX XXXXXXXXX XX the range &XX;>&XX;>>>&XX;>&XX;</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">&XX;&XX;&XX;&XX;<<&XX;&XX;<&XX;<&XX;&XX;<&XX;<&XX;<<&XX;&XX;&XX;&XX;&XX;&XX;&XX;&XX;&XX;&XX;<&XX;&XX;&XX;O</span></p> <p><span class="s1">-10<span XXXXX="XXXXX-XXXXXXXXX-space"> </span>-9<span XXXXX="XXXXX-converted-space"> </span>-X <span class="XXXXX-converted-XXXXX"> </span>-7<span XXXXX="XXXXX-XXXXXXXXX-space"> </span>-6 <span class="XXXXX-converted-space"> </span>-X <span class="XXXXX-converted-space"> </span>-X<span XXXXX="Apple-XXXXXXXXX-space"> </span>-3 <span class="XXXXX-converted-space"> </span>-2 <span XXXXX="Apple-converted-XXXXX"> </span>-1<span XXXXX="Apple-converted-XXXXX"> </span>X<span XXXXX="Apple-converted-space"> </span>X <span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>2 <span XXXXX="Apple-XXXXXXXXX-space"> </span>3<span class="XXXXX-XXXXXXXXX-XXXXX"> </span>4<span XXXXX="Apple-converted-XXXXX"> </span>X<span XXXXX="Apple-converted-XXXXX"> </span>6<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>X<span class="XXXXX-XXXXXXXXX-space"> </span>X<span XXXXX="Apple-converted-space"> </span>9<span XXXXX="Apple-converted-XXXXX"> </span>XX</span></p> <p><span class="XX">|XXXX|____|____|XXXX|____|XXXX|XXXX|XXXX|____|XXXX|XXXX|XXXX|XXXX|____|XXXX|XXXX|XXXX|____|____|____|</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">(c)</span></p> <p><span XXXXX="s1">X - 4x > XX</span></p> <p><span class="XX">-XX &XX; XX</span></p> <p><span XXXXX="XX">x &XX; XX/-X</span></p> <p><span class="s1">x < -3</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">The XXXXXXXX XX indicated by the XXXXX >&XX;>&XX;&XX;&XX;&XX;&XX;&XX;</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"><<&XX;<&XX;<<<<&XX;&XX;<&XX;&XX;&XX;<&XX;&XX;<<&XX;&XX;&XX;<<<<</span></p> <p><span class="s1">-XX<span XXXXX="Apple-converted-XXXXX"> </span>-X<span class="XXXXX-converted-space"> </span>-X <span XXXXX="Apple-converted-XXXXX"> </span>-X<span XXXXX="XXXXX-XXXXXXXXX-space"> </span>-X <span class="XXXXX-XXXXXXXXX-space"> </span>-X <span XXXXX="Apple-converted-XXXXX"> </span>-X<span class="Apple-converted-space"> </span>-3 <span class="XXXXX-converted-space"> </span>-2 <span XXXXX="Apple-XXXXXXXXX-space"> </span>-X<span class="XXXXX-XXXXXXXXX-space"> </span>X<span class="Apple-converted-space"> </span>X <span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>2 <span XXXXX="XXXXX-converted-space"> </span>3<span class="Apple-XXXXXXXXX-XXXXX"> </span>X<span class="XXXXX-converted-XXXXX"> </span>5<span XXXXX="XXXXX-converted-space"> </span>X<span XXXXX="XXXXX-converted-XXXXX"> </span>X<span XXXXX="XXXXX-converted-XXXXX"> </span>8<span class="XXXXX-XXXXXXXXX-space"> </span>9<span class="XXXXX-converted-XXXXX"> </span>XX</span></p> <p><span class="s1">|____|____|____|XXXX|____|XXXX|XXXX|XXXX|XXXX|____|XXXX|XXXX|____|XXXX|XXXX|XXXX|____|____|____|____|</span></p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX">(d)</span></p> <p><span class="XX"></span> </p> <p><span class="s1">8x - 6(x-X) > XX - 2x</span></p> <p><span class="XX">8x - XX + XX &XX; 20 - XX</span></p> <p><span XXXXX="XX">2x + 12 &XX; XX - XX</span></p> <p><span class="XX">4x > 20 - 12</span></p> <p><span class="XX">XX > X</span></p> <p><span XXXXX="s1">x &XX; X</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"><span class="Apple-XXXXXXXXX-space"> </span>&XX;&XX;>>>>>&XX;>>&XX;&XX;&XX;>>&XX;>&XX;>&XX;&XX;>&XX;&XX;&XX;&XX;</span></p> <p><span XXXXX="XX">-10<span class="Apple-XXXXXXXXX-XXXXX"> </span>-9<span XXXXX="Apple-converted-XXXXX"> </span>-X <span XXXXX="XXXXX-converted-XXXXX"> </span>-7<span class="XXXXX-XXXXXXXXX-XXXXX"> </span>-6 <span class="XXXXX-converted-XXXXX"> </span>-X <span XXXXX="XXXXX-converted-XXXXX"> </span>-X<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>-3 <span XXXXX="XXXXX-converted-XXXXX"> </span>-2 <span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>-X<span XXXXX="Apple-converted-space"> </span>X<span class="Apple-converted-XXXXX"> </span>X <span XXXXX="Apple-converted-XXXXX"> </span>2 <span class="XXXXX-converted-XXXXX"> </span>X<span class="XXXXX-converted-space"> </span>4<span XXXXX="XXXXX-XXXXXXXXX-space"> </span>X<span class="Apple-converted-XXXXX"> </span>6<span class="Apple-XXXXXXXXX-space"> </span>X<span class="XXXXX-converted-space"> </span>8<span class="XXXXX-XXXXXXXXX-XXXXX"> </span>X<span class="Apple-XXXXXXXXX-XXXXX"> </span>10</span></p> <p><span class="s1">|____|____|XXXX|____|XXXX|XXXX|XXXX|XXXX|____|____|XXXX|XXXX|XXXX|XXXX|____|____|XXXX|XXXX|____|XXXX|</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">(e)</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s2">X (2x + X)</span><span class="XX"> &XX; </span><span class="s2">X </span><span class="XX">x + X</span></p> <p><span class="s1"><span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>X <span XXXXX="XXXXX-converted-XXXXX"> </span>X</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">X (2x + X) &XX; XX + XX</span></p> <p><span XXXXX="XX">XX + 6 &XX; XX + XX</span></p> <p><span class="XX">4x &XX; X</span></p> <p><span class="s1">x > X.5</span></p> <p><span class="s1"></span> </p> <p><span class="s1"><span class="Apple-XXXXXXXXX-space"> </span>&XX;>>>&XX;>>&XX;>&XX;>&XX;>>&XX;&XX;>>&XX;&XX;>&XX;>>&XX;>></span></p> <p><span XXXXX="XX">-XX<span class="XXXXX-XXXXXXXXX-space"> </span>-X<span XXXXX="Apple-XXXXXXXXX-space"> </span>-X <span XXXXX="Apple-converted-space"> </span>-X<span class="Apple-converted-XXXXX"> </span>-6 <span class="Apple-converted-space"> </span>-X <span XXXXX="Apple-converted-space"> </span>-X<span class="Apple-converted-XXXXX"> </span>-3 <span class="Apple-converted-XXXXX"> </span>-2 <span class="XXXXX-XXXXXXXXX-XXXXX"> </span>-X<span XXXXX="Apple-converted-XXXXX"> </span>0<span XXXXX="Apple-converted-XXXXX"> </span>X <span XXXXX="Apple-converted-XXXXX"> </span>X <span class="Apple-XXXXXXXXX-space"> </span>X<span XXXXX="XXXXX-converted-space"> </span>4<span class="Apple-converted-space"> </span>X<span XXXXX="XXXXX-converted-XXXXX"> </span>6<span class="XXXXX-XXXXXXXXX-space"> </span>X<span class="XXXXX-converted-space"> </span>X<span XXXXX="XXXXX-converted-space"> </span>9<span class="XXXXX-converted-space"> </span>10</span></p> <p><span class="XX">|____|____|XXXX|____|XXXX|XXXX|____|____|XXXX|____|____|XXXX|____|____|____|XXXX|____|____|____|____|</span></p> <p><span class="XX"></span> </p> <p><span class="s1">Applications</span></p> <p><span XXXXX="s1">2. (a)<span XXXXX="XXXXX-XXXXXXXXX-space"></span></span></p> <p><span XXXXX="XX">XXXXX will pay XX + 5.25n</span></p> <p><span XXXXX="XX">Edwin XXXX XXX XXXX than XXXX if:</span></p> <p><span class="XX">XX + X.XXX &XX; XXX</span></p> <p><span XXXXX="XX">Solving the XXXXXXXXXX:</span></p> <p><span class="s1">5.25n > XXX - XX</span></p> <p><span XXXXX="s1">X.25n &XX; XX</span></p> <p><span class="XX">n > XX</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">(b)<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"></span></span></p> <p><span XXXXX="XX">Edwin XXX XXXX 11 XXXXX and XXXXX pay XXXX than XXXX. This is because XX will make XXXX XXXXX, and 13 or XXXXX XXXX XXXX XXXXX XX pay more XXXX XXXX.</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">XXXXXXXXX</span></p> <p><span class="XX">3. (a) XX + b ≥ cd</span></p> <p><span class="s1">ax ≥ cd - b</span></p> <p><span class="s1">x ≥ (cd - b) / a</span></p> <p><span class="XX"></span> </p> <p><span class="XX">(b)<span XXXXX="Apple-converted-space"></span></span></p> <p><span class="s2">a (x + 2) </span><span XXXXX="XX">> c</span></p> <p><span XXXXX="XX"><span XXXXX="XXXXX-XXXXXXXXX-space"> </span>b <span class="Apple-XXXXXXXXX-XXXXX"></span></span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">XX + 2a > XX</span></p> <p><span XXXXX="XX">x > </span><span XXXXX="s2">bc - 2a<span class="Apple-converted-space"></span></span></p> <p><span class="s1"><span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>a<span class="XXXXX-converted-space"></span></span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">X. The correct XXXXXX is (X)<span class="Apple-converted-XXXXX"></span></span></p> <p><span class="s1">XX + b > d</span></p> <p><span class="s1">x > (d - b) /a</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">≥ ≤</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">97150</span></p> <p><span class="s1">XXXXXXXX X: XXXXXX XXX XXXXXXXXXXXXXXX/Dictatorship: A Study XX XXXXX Korea<span class="Apple-XXXXXXXXX-XXXXX"></span></span></p> <p><span XXXXX="s1">What XXXXXXXXXX XXXXXXX XXX you provide XX the XXXXX Korean XXXXXXXXXX XXXX is XXXXXXXXXX with the XXXXXXXX issue you chose?</span></p> <p><span class="s1"></span> </p> <p><span class="XX" <XXX="" enduring="" XXXXX="" that="" XXXX="" interests="" XX="" XX="" the="" of="" XXXXX="" XXXXXX.="" according="" to="" XX,="" XXXXXX="" are="" XXXXXX="" XXX="" people,="" regardless="" their="" XXXXXX,="" XXXXXX="" XXXXXX,="" XXXXXX="" XXXXXXXX,="" linguistic="" XXXXXXXXXX,="" XXXXX="" or="" XXXXX="" demographic="" identifiers.="" these="" include="" XXXXX="" life="" XXX="" freedom,="" freedom="" from="" torture="" XXXXXXXXXXX,="" express="" XXXXX,="" XXXXX="" XXXX="" XXX="" a="" XXXX="" XXXX,="" so="" XX.="" north="" korea’s="" XXXXXXXXXX="" context="" grim,="" its="" record="" XXXXXX.="" passage,="" 2014="" un="" XXXXXXXXXX="" inquiry="" XXXXX="" XXXXXXXXXX="" committed="" XXXXX,="" XXXXXXXXXX="" widespread="" abuses,="" XXXXXXXXX="" XXXXXXXXXXXXX,="" XXXXXXX,="" XXXX="" XXXXXXXXXXXX.="">span class="Apple-XXXXXXXXX-XXXXX"&XX;</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">XXXXX Korea XXX XXXXXX out XX the repressive XXXXXXXXXX XX Kim XX-Sung, a XXXX-war XXXXXXXXXXX communist who XXXXXXXXX the civil liberties of XXX North XXXXXX XXXXXX in order to XXXX with national XXXXXXXXXXX XXXX XX XXX XXXXXX War. XXXXXXXXXXX, XXX XX-Sung and XXX descendants XXXX continued to consolidate XXXXX in a XXX that XXXXXXXX human XXXXXX in North XXXXX. They have XXXXXXX a XXXXXX XXXXX free XXXXXX is XXXXXXXXXX, and where judicial XXXXXXXXX routinely abuse human XXXXXX. XXXXX include XXX use XX torture, forced XXXXX and XXXXXXXXXXXXX in inhumane XXXXXXXXXX. There is XXXX no XXXXXXXXXXX due process within the judicial XXXXXX. The XXXX of XXXXX XXXXXX in XXXXX Korea is a XXXXXX of XXXXXXX of consolidation XX the XXXXX XXXXXX XXXXXXXXX dictatorship, in a bid to XXXXXXXX their XXXX grip XX XXXXX over XXX country.<span class="Apple-converted-XXXXX"></span></span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">XXX does XXX issue of power/human XXXXXX in XXX XXXXXXXXXX XX North Korea XXXXXX XXXXXX?</span></p> <p><span class="s1"></span> </p> <p><span class="s1" <the="" north="" korean="" XXXXXX="" XXX="" XXXXXXXX="" in="" three="" main="" ways:="" famine,="" inhumane="" XXXXXXXXXXXX="" and="" XXXXXX="" labor.="" XXXXXXXX,="" chronic="" mismanagement="" of="" XXX="" economy="" has="" led="" to="" XXXXXXXXXX="" multiple="" XXXXXXX="" over="" XXXXX="" lifetime.="" XXXX="" deprived="" them="" freedom="" work="" live.="" XXXXXXXXXXX,="" XXXXXXX="" XXXXXX="" access="" XXXX="" media="" XXXX="" as="" XXX="" XXXX="" times,="" XXXXX="" XXXXXX="" right="" XXXXXX.="" also="" not="" move,="" with="" movement="" XXXXXXX="" XXXXXX="" XXXXXXXXXXX="" XXXXX="" XXXXXXX="" border="" XXXXXXXX="" XXXXXXXX="" XXXXXXXXXXX.="" finally,="" XXXXXXXXX="" prisoners="" XXXXXXXXX="" have="" human="" XXXXXX="" XXXXXXXX="" XXXXX,="" XXXXXXX,="" XXXXX="" conditions.="" XXXXX="" XXXXXXX,="" korea="" XXXXXXXX="" XXXXXXXXX="" prison="" camps="" XXXXX="" XXXXXXXXX="" opponents="" XXXXXXXXXX="" sent="" face="" starvation="" rations="">span class="Apple-converted-space"&XX;</span></p> <p><span XXXXX="s1">94233</span></p> <p><span XXXXX="s1">XXXXXXX equations</span></p> <p><span XXXXX="s1">1a. x - X = 8</span></p> <p><span class="XX">x = X + X</span></p> <p><span XXXXX="s1">x = 15</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">XX. x - b = a</span></p> <p><span XXXXX="XX">x = a + b</span></p> <p><span class="s1"></span> </p> <p><span class="XX">2a.<span class="XXXXX-converted-space"> </span>4x = -12</span></p> <p><span XXXXX="XX">x = -3</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">XX. -3k = m</span></p> <p><span class="XX">X = m/(-X)<span class="Apple-XXXXXXXXX-space"></span></span></p> <p><span XXXXX="XX">X = </span><span XXXXX="s2">-X <span class="Apple-XXXXXXXXX-XXXXX"></span></span><span XXXXX="s1"> m</span></p> <p><span XXXXX="s1"><span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>3</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">XX. 2x - X = XX</span></p> <p><span XXXXX="XX"><span class="Apple-converted-space"> </span>x = (XX + X)/2 = 8</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">XX. 2b - 9 = d</span></p> <p><span class="s1"><span XXXXX="Apple-converted-XXXXX"> </span>b = (d + 9) / 2</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">4a. X/2<span class="Apple-XXXXXXXXX-space"> </span>(XX) = -XX</span></p> <p><span XXXXX="XX"><span class="XXXXX-converted-space"> </span>4x = -XX</span></p> <p><span class="XX"><span XXXXX="XXXXX-XXXXXXXXX-space"> </span>x = -10</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">4b. XXX = XX</span></p> <p><span class="s1"><span XXXXX="Apple-converted-space"> </span>g = 10 / XX</span></p> <p><span class="s1"></span> </p> <p><span class="XX">XX. x / -8 = XX</span></p> <p><span class="s1"><span XXXXX="Apple-converted-XXXXX"> </span>x = - 88</span></p> <p><span XXXXX="s1"></span></p> <p><span class="s1">XX. y/3 = h</span></p> <p><span class="XX"><span class="XXXXX-XXXXXXXXX-XXXXX"> </span>y = XX<span class="Apple-XXXXXXXXX-XXXXX"></span></span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">XXXXX</span></p> <p><span XXXXX="XX">XXXXXXXX 4: Modern Day XXXXXXXXXXXXXXX/Dictatorship: A Study of North Korea<span XXXXX="XXXXX-converted-space"></span></span></p> <p><span class="s1">What XXXXXXXXXX context XXX you provide XX XXX XXXXX XXXXXX Government that is XXXXXXXXXX with XXX enduring issue you chose?</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX" <XXX="" XXXXXXXX="" issue="" XXXX="" most="" interests="" XX="" is="" XXX="" of="" XXXXX="" XXXXXX.="" XXXXXXXXX="" to="" XX,="" XXXXXX="" are="" XXXXXX="" XXX="" people,="" regardless="" XXXXX="" gender,="" XXXXXX="" origin,="" ethnic="" XXXXXXXX,="" XXXXXXXXXX="" background,="" XXXXX="" or="" other="" XXXXXXXXXXX="" identifiers.="" these="" XXXXXXX="" XXXXX="" life="" and="" XXXXXXX,="" XXXXXXX="" from="" XXXXXXX="" enslavement,="" express="" XXXXX,="" XXXXX="" work="" for="" a="" fair="" wage,="" so="" on.="" north="" XXXXX’s="" historical="" XXXXXXX="" XXXX,="" its="" record="" dismal.="" XXXXXXX,="" 2014="" un="" XXXXXXXXXX="" inquiry="" XXXXX="" XXXXXXXXXX="" XXXXXXXXX="" XXXXX,="" systematic="" widespread="" abuses,="" XXXXXXXXX="" extermination,="" XXXXXXX,="" XXXX="" imprisonment.="">span XXXXX="XXXXX-converted-XXXXX"></span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">XXXXX Korea XXX XXXXXX out XX the XXXXXXXXXX government of Kim XX-XXXX, a XXXX-war nationalist XXXXXXXXX who suspended the XXXXX liberties of XXX North Korean people in order to XXXX XXXX national emergencies such as XXX XXXXXX War. Furthermore, Kim Il-Sung XXX XXX XXXXXXXXXXX have XXXXXXXXX to XXXXXXXXXXX XXXXX in a way XXXX curtails human XXXXXX in North XXXXX. XXXX have created a regime where free speech is XXXXXXXXXX, XXX where XXXXXXXX XXXXXXXXX XXXXXXXXX XXXXX human rights. These include XXX XXX XX torture, XXXXXX labor and incarceration in inhumane conditions. XXXXX is also XX XXXXXXXXXXX due XXXXXXX within the XXXXXXXX system. XXX XXXX of human rights in XXXXX Korea XX a XXXXXX of decades XX XXXXXXXXXXXXX by the North Korean communist dictatorship, in a bid to continue XXXXX firm grip XX XXXXX over XXX country.<span class="Apple-XXXXXXXXX-space"></span></span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">XXX does XXX issue of power/human XXXXXX in XXX government of North Korea XXXXXX XXXXXX?</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1" <XXX="" XXXXX="" korean="" people="" are="" affected="" in="" XXXXX="" main="" XXXX:="" famine,="" inhumane="" imprisonment="" and="" XXXXXX="" labor.="" XXXXXXXX,="" chronic="" XXXXXXXXXXXXX="" of="" XXX="" XXXXXXX="" XXX="" XXX="" XX="" XXXXXXXXXX="" multiple="" XXXXXXX="" over="" their="" lifetime.="" this="" deprived="" XXXX="" XXXXXXX="" work="" XXXX.="" furthermore,="" koreans="" XXXXXX="" access="" free="" XXXXX="" such="" as="" new="" york="" times,="" XXXXX="" XXXXXX="" right="" XXXXXX.="" XXXX="" not="" move,="" XXXX="" movement="" XXXXXXX="" XXXXXX="" XXXXXXXXXXX="" XXXXX="" through="" border="" XXXXXXXX="" XXXXXXXX="" checkpoints.="" XXXXXXX,="" political="" prisoners="" routinely="" XXXX="" human="" XXXXXX="" violated="" labor,="" XXXXXXX,="" XXXXX="" XXXXXXXXXX.="" noted="" passage,="" XXXXX="" operates="" secretive="" XXXXXX="" camps="" XXXXX="" perceived="" opponents="" XXXXXXXXXX="" sent="" XXXX="" XXXXXXXXXX="" rations="">span class="XXXXX-converted-space"></span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">84417</span></p> <p><span XXXXX="s1">Unit X XXXX</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX"><span XXXXX="Apple-converted-space"></span>X. 1.<span class="XXXXX-XXXXXXXXX-XXXXX"></span></span></p> <p><span XXXXX="XX">8. X.</span></p> <p><span XXXXX="XX">9. 2.</span></p> <p><span XXXXX="s1">10. X.</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">XXXXX</span></p> <p><span class="s1">XXXXXXX XXXXXXXXX: Worksheet #X</span></p> <p><span XXXXX="s1">6a.<span class="XXXXX-XXXXXXXXX-space"></span></span></p> <p><span class="s1">14 = 2x + 26</span></p> <p><span XXXXX="XX">XX = 26 - 14</span></p> <p><span class="s1">x = XX / X</span></p> <p><span class="s1">x = 6</span></p> <p><span class="s1"></span> </p> <p><span class="XX">XX. XX = XX + X</span></p> <p><span class="s1">XX = 3d - 5</span></p> <p><span XXXXX="s1">v = (XX - 5) /X</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">7a. -30 = 4 - XX</span></p> <p><span XXXXX="XX"><span XXXXX="Apple-converted-XXXXX"> </span>XX = 4 + XX</span></p> <p><span XXXXX="s1"><span class="XXXXX-XXXXXXXXX-space"> </span>x = 34/X</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">XX. 7a = 10 - XX</span></p> <p><span class="s1"><span class="XXXXX-converted-XXXXX"> </span>2h = XX - XX</span></p> <p><span XXXXX="XX"><span class="Apple-XXXXXXXXX-space"> </span>h = (10 - 7a) /X</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">XX. X(x-X) = XX</span></p> <p><span XXXXX="XX"><span class="Apple-XXXXXXXXX-space"> </span>3x - XX = 12</span></p> <p><span class="s1"><span class="XXXXX-XXXXXXXXX-XXXXX"> </span>XX = 24</span></p> <p><span class="s1"><span class="Apple-converted-XXXXX"> </span>x = X</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">8b. 5(XX + p) = w</span></p> <p><span class="XX"><span class="XXXXX-converted-XXXXX"> </span>20x + 5p = w</span></p> <p><span XXXXX="XX"><span class="XXXXX-converted-space"> </span>5p = w - 20x</span></p> <p><span XXXXX="s1"><span class="Apple-converted-space"> </span>p = (w - 20x) / 5<span class="XXXXX-XXXXXXXXX-XXXXX"></span></span></p> <p><span class="XX"></span> </p> <p><span class="XX">XXXXX is XXXXXXXXXX to 7a - 8b = XXX</span></p> <p><span XXXXX="s1">a = (XXX + 8b) / 7</span></p> <p><span XXXXX="XX">XXX XXXXXX XX X</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">XXXXX XX XXXXXXXXXX to XXX + X = XX</span></p> <p><span class="XX">X = XX - XXX</span></p> <p><span XXXXX="s1">XXX XXXXXX XX X</span></p> <p><span XXXXX="XX"></span> </p><p><br></p>">
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