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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-XXXXXXXXX-space"></span></span></p> <p><span XXXXX="XX">This XXXXXX is XXXXX.</span></p> <p><span XXXXX="s1"></span></p> <p><span XXXXX="XX">(b) Let Evie’s age now be x, and her XXXXXX’s age XX XXXXXXX XXXX be x + XX.</span></p> <p><span XXXXX="s1">Let Evie’s age three XXXXX from now XX x + X, and her XXXXXX’s age 3 XXXXX from XXX XX 5x + 15, or also, x + XX + X = x + XX</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">Three years from XXX: her XXXXXX’s age is XXXXX XX:</span></p> <p><span class="s1">5x + XX = x + 39</span></p> <p><span class="s1">4x = XX</span></p> <p><span class="XX">x = 6</span></p> <p><span class="s1">Hence, XXXX XX X XXXXX old now.</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">XXXXXXXX #X</span></p> <p><span class="s1">Kirk = x, XXX = y</span></p> <p><span class="s1">XXXXXXXX 1: <span class="Apple-tab-span"> </span><span class="XXXXX-tab-span"> </span>x + XX = y</span></p> <p><span XXXXX="s1">EQUATION X: <span class="Apple-tab-span"> </span><span XXXXX="Apple-tab-span"> </span>(1/2) y = x - 2</span></p> <p><span class="XX">Let XXXXXXXX 2 XX XXXXXXXXXXX XXXX EQUATION X (multiply both sides XX X): y = 2x - X</span></p> <p><span class="XX">XXXXXXXXX, equating XXXXXXXX 1 XXX XXXXXXXX 3:</span></p> <p><span XXXXX="XX">x + 12 = 2x - 4</span></p> <p><span class="s1">x = 16</span></p> <p><span class="XX">y = x + 12 = XX + XX = 28</span></p> <p><span class="s1">XXXX has 16 XXXXXXX, XXX has XX XXXXXXX</span></p> <p><span class="s1"></span> </p> <p><span class="XX">FLUENCY</span></p> <p><span XXXXX="XX">X. (X) The XXXXX equation, XX + (XX -X) = 15 , could be used to find the XXXXX of XXX XXXXXX n. XXXX XX XXXXXXX XXX first XXXXXXXX contains XXX XXX of XXXXX XXXXX a XXXXXX XXX 2 XXXX XXXX X times that XXXX XXXXXX, XXX XXXXX XXXXX sum and XXXXXXX it to the target XXXXXX of XX.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">X.</span></p> <ol> <li><span XXXXX="XX">XXX the XXX of 3 less than 5 times a XXXXXX and the XXXXXX XXXXXXXXX XX X XXXXXXXXX 24 XX:</span></li> </ol> <p><span class="XX">5x - 3 + (x+9) = 24</span></p> <p><span class="s1">XXXXXXX XXX equation:</span></p> <p><span class="s1">6x + X = XX</span></p> <p><span XXXXX="s1">x = XX/6 = 3</span></p> <p><span class="s1"></span> </p> <p><span class="XX">(b) Let Tom’s age XX t, Andrew’s age be a, XXXX’s age XX s. XXX equations XXX XX XXXXXXX:</span></p> <p><span XXXXX="XX">t =<span class="XXXXX-converted-XXXXX"> </span>XX + X</span></p> <p><span XXXXX="XX">s = XX - X<span XXXXX="Apple-converted-space"></span></span></p> <p><span class="XX">t = s XXXXXXX XXX XXX Sara are XXXXX.</span></p> <p><span XXXXX="s1">2a + X = XX - X</span></p> <p><span class="XX">3a = 12</span></p> <p><span class="XX">a = X</span></p> <p><span class="XX">t= 2(4) + 4 = XX</span></p> <p><span class="s1">s = 20 - X = 12<span class="Apple-XXXXXXXXX-space"> </span></span></p> <p><span XXXXX="XX">XXXXXX is X XXXXX old.<span class="XXXXX-XXXXXXXXX-space"></span></span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">(c) XXXXX months XX use = x, x=X and XXXX XX XXXX XX XXXXX XX $35(x) + $XX.50 = $XX.XX, XXX total texts are XXX, cost XXX text is XX.5/450 = $X.XXX.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">(d)<span XXXXX="XXXXX-converted-XXXXX"> </span>Daniel’s son’s age is x, XXXXXX’s age is x + XX. In six XXXXX, Daniel ’s XXX will XX x+X, XXXXXX will be X(x+X) or x + 26 + 6 = x + XX.</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">Hence, let Daniel’s age in X XXXXX be either X(x+6) or x + 32.</span></p> <p><span class="s1">Equating XXXX XXXXXXXXXXXXX for XXXXXX’s age in 6 XXXXX, we XXX:</span></p> <p><span XXXXX="s1">3(x+6) = x + 32</span></p> <p><span XXXXX="XX">XX + XX = x + XX</span></p> <p><span XXXXX="XX">3x - x = XX</span></p> <p><span class="s1">2x = XX</span></p> <p><span class="s1">Daniel’s son’s present age: x = 7 XXXXXX’s XXXXXXX age: x + 26 = 33</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">XXXXXXXXX, Daniel’s son XX 7 XXX Daniel XX 33.<span XXXXX="Apple-converted-XXXXX"></span></span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">XXXXXXXXXXXX</span></p> <p><span class="s1">X. XXX age XX XXXXXXX XX x, XXXX be X(x-XX), XXXXX be XX - 12, XXXX be 0.XX + 6</span></p> <p><span XXXXX="s1">XXX XXXXX XX XXXXX ages is given by the XXXXXXXX:</span></p> <p><span class="XX">x + 2(x - XX) + 2x - XX + X.XX + X = XXX</span></p> <p><span XXXXX="s1">x + XX - XX + 2x - XX + 0.XX + X = 106</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">X.XX = 132</span></p> <p><span class="s1">x = 24 (XXXXXXXXX, manager XX 24)</span></p> <p><span XXXXX="s1">Kirk XX X(XX-10) = XX years XXX.</span></p> <p><span class="XX">XXXXX XX X(XX) - 12 = XX years old.</span></p> <p><span XXXXX="s1">XXXX is 0.5(XX) + X = 18 XXXXX XXX.</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">XXXXXXXXX</span></p> <p><span XXXXX="s1">XXX 0.XXX+XX = 0.XXX + 18.5</span></p> <p><span class="XX">0.XXX = -X.5</span></p> <p><span XXXXX="s1">x = -XXX</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">XXXXX XXX XXXXXXX, the two XXXXX XXXX XXXXXX the same amount.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">XXXX means XXXX XXXXXXX’s XXXX XX generally more XXXXXXXXX XXXX XXXXXXX’s plan.</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="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="XX"></span> </p> <p><span XXXXX="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 class="XX"></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 class="s1"></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 XXXXX="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 XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></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="XX"></span> </p> <p><span XXXXX="XX"></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="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="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"></span> </p> <p><span XXXXX="XX">428CCAlg1U2L2SeeingStructuretoSolveEquations<span XXXXX="Apple-XXXXXXXXX-XXXXX"></span></span></p> <p><span XXXXX="s1">SEEING XXXXXXXXX XX XXXXX EQUATIONS XXXXXX XXXX XXXXXXX I</span></p> <p><span class="XX"></span> </p> <p><span class="s1">XXXXXXXX #X</span></p> <ol> <li><span class="s1">x was multiplied by 5 XXX XXXXXXXXX XX 3, XXX then the entire XXXX XXXX side XX the XXXXXXXX XXX equated to XX.</span></li> <li><span XXXXX="XX"> XX + 3 = 23</span></li> </ol> <p><span class="XX">5x = XX - X</span></p> <p><span XXXXX="s1">XX = XX</span></p> <p><span XXXXX="XX">x = X</span></p> <p><span class="XX"></span> </p> <p><span class="XX">Exercise #2</span></p> <p><span XXXXX="XX">(a) What XXXXXXXX to x? x was XXXXXXX XX X, XXXXXXX XX X and X XXX added to the XXXXXX sum. XX was then equated XX -6.<span XXXXX="Apple-XXXXXXXXX-space"></span></span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s2">x - X</span><span XXXXX="XX"> + X = XX</span></p> <p><span class="s1"><span class="Apple-XXXXXXXXX-XXXXX"> </span>X</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">x - X + 14 = 46</span></p> <p><span class="s1">x = XX - XX + 3</span></p> <p><span XXXXX="s1">x = XX</span></p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">(b) What happened XX x? x XXX XXXXXXXXX by X, x+1 was multiplied XX 4, and XXX whole XXX XXX XXXXXXX by 2. It XXX XXXX equated to -6.</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">X(x+1) - X = -6</span></p> <p><span class="s1">4x + 4 - X = -X</span></p> <p><span class="XX">4x = -X + X - X</span></p> <p><span XXXXX="XX">4x = -8</span></p> <p><span XXXXX="s1">x = -X</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">Exercise #X</span></p> <p><span class="XX">(a) -X (x - X) + 8 = 2</span></p> <p><span class="s1"><span XXXXX="XXXXX-tab-span"> </span>-X(x-4) + 6 = 0</span></p> <p><span XXXXX="XX"><span class="Apple-tab-span"> </span>-X (x-X) = -X</span></p> <p><span XXXXX="s1"><span XXXXX="Apple-tab-span"> </span>(x-X) = 3</span></p> <p><span XXXXX="XX"><span XXXXX="Apple-tab-span"> </span>x = 4+X</span></p> <p><span XXXXX="s1"><span XXXXX="Apple-tab-span"> </span>x = 7</span></p> <p><span XXXXX="s1">(b) XXXXXXXXXXXX XXXXXXXX</span></p> <p><span class="XX">-X (x - X) + X = 2</span></p> <p><span XXXXX="XX"><span class="XXXXX-tab-span"> </span>-2x + 8 + 8 = X</span></p> <p><span XXXXX="s1"><span class="Apple-tab-span"> </span>-XX = -14</span></p> <p><span class="XX"><span XXXXX="XXXXX-tab-span"> </span>x = -14/-2</span></p> <p><span class="s1"><span XXXXX="XXXXX-tab-span"> </span>x = X</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">Exercise #X</span></p> <p><span class="s1">(a) XXXXXXX up XXX equation: 5x - 10 = 35</span></p> <p><span XXXXX="s1"><span class="XXXXX-tab-span"> </span>5x = XX</span></p> <p><span class="s1"><span XXXXX="Apple-tab-span"> </span>x = 9</span></p> <p><span class="XX">XXXXXXXXXXXX x = X XXXX the original XXXXXXXX</span></p> <p><span XXXXX="XX">5 (9) - XX = 35</span></p> <p><span XXXXX="XX" <XXX="" equation="" holds,="" so="" XXX="" answer="" is="" XXXXXXX.="">span class="Apple-XXXXXXXXX-space"&XX;</span></p> <p><span XXXXX="XX">(b) Setting up the equation: (X(x+7)) + XX = 4</span></p> <p><span XXXXX="XX">XXXXX XXX distribution XXXXXX:</span></p> <p><span class="XX">XX + 21 + XX = 4</span></p> <p><span class="s1">XX = X- XX - XX</span></p> <p><span class="s1">3x = - 27</span></p> <p><span XXXXX="XX">x = -9</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">Fluency</span></p> <p><span class="s1">X. x/X - X is comprised of x XXXXXXX XX X, XXX reduced (XXXXXXXXXX) by X.</span></p> <p><span XXXXX="XX">XXXXX, the XXXXXXX XXXXXX is (X).</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">2. 6x + X = 4</span></p> <p><span class="XX">XX = 4 - X</span></p> <p><span class="XX">6x = X</span></p> <p><span XXXXX="XX">x = 3/X = X/2</span></p> <p><span XXXXX="s1">The answer XX (X)</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">X. 5(x-X) - 6 = 24</span></p> <p><span class="s1">X(x-2) = 24 + X</span></p> <p><span XXXXX="XX">5x - 10 = 30</span></p> <p><span class="s1">5x = 40</span></p> <p><span class="s1">x = 40/5 = 8</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">The XXXXXXX XXXXXX XX (X)</span></p> <p><span class="s1"></span> </p> <p><span class="XX"><b>XXXXXXXXXXXX</b></span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">4.<span XXXXX="Apple-XXXXXXXXX-space"></span></span></p> <p><span XXXXX="XX">(x + X) </span><span class="XX">= 7</span></p> <p><span class="XX"><span class="XXXXX-XXXXXXXXX-XXXXX"> </span>X</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">x + 5 = 21</span></p> <p><span class="s1">x = 21 - X</span></p> <p><span class="s1">x = 16</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">5. In the XXXXXXX, XXX XXX’s age be m, XXXX’s age XX X. <span XXXXX="XXXXX-XXXXXXXXX-XXXXX"></span></span></p> <p><span class="XX">XXX us set XX XXX equation.</span></p> <p><span class="s1">X(m-3) + X = 26<span class="XXXXX-converted-XXXXX"></span></span></p> <p><span class="XX"></span> </p> <p><span class="XX">z = 8</span></p> <p><span XXXXX="XX">Substituting z = X</span></p> <p><span class="s1">2 (m - 3) + X = 26</span></p> <p><span XXXXX="XX">2m - X + X = XX</span></p> <p><span class="s1">2m = XX + X - 8</span></p> <p><span XXXXX="s1">2m = XX</span></p> <p><span class="s1">m = XX</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">XXX XXXXXX is correct because m - 3 = 9, to XXXXXX it XX XX, and to add it XX 8 XX 26.</span></p> <p><span class="XX"></span> </p> <p><span class="s1">The XXXXXXXX XXXXX.</span></p> <p><span class="s1"></span> </p> <p><span class="s1">X.<span XXXXX="Apple-XXXXXXXXX-space"> </span>(a) X = XX + XX</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">(b) F = 2W + XX</span></p> <p><span XXXXX="XX">X = 2(12) + X(20)</span></p> <p><span XXXXX="XX">F = XX</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">(c) XX X = 120, XXX X = 30, XXXX:</span></p> <p><span class="s1">XXX = 2W + 2(XX)</span></p> <p><span class="XX">XX = XX</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">X. (a) x was XXXXXXXXXX by 2, the XXXXXX XXX XXXXXXX XX X, XXX result was multiplied XX X, the XXXXXX XXX divided XX X, XXX result XXX XXXXXXX by X, XXX result was equated XX 11.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">(b) </span><span XXXXX="s2">X (XX - X) </span><span XXXXX="XX">- 4 = 11</span></p> <p><span XXXXX="XX"><span class="Apple-tab-span"> </span>3</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">XXXXXXXX everything by X, XXXXXX XXXX hand XXXX XX XXX XXXXXXXX</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">XXX - X - XX = XX</span></p> <p><span class="XX">10x = 50</span></p> <p><span class="s1">x = XX/10</span></p> <p><span class="XX">x = X</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">X. (a) x XXX multiplied by 3, XXX XXXXXX was XXXXX XX X, the XXXXXX was XXXXXXXXXX XX X, XXX result was XXXXXXX to -16.</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">X(XX + X) = -XX</span></p> <p><span class="s1">3x + X = -64</span></p> <p><span XXXXX="XX">XX = -66</span></p> <p><span class="s1">x = -22</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">(b) X(3x + X) = -16</span></p> <p><span XXXXX="XX">XXX + X = -XX</span></p> <p><span XXXXX="s1">XXX = -24</span></p> <p><span XXXXX="XX">x = -X</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="XX"></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 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="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="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 class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></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="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 class="XX"></span> </p> <p><span XXXXX="s1"></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="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">XXXXXXXXXXXXXXXXXXXXXXXXX<span XXXXX="Apple-XXXXXXXXX-XXXXX"></span></span></p> <p><span XXXXX="s1">INEQUALITIES (JUST ANOTHER TRUE/XXXXX QUESTION) XXXXXX XXXX ALGEBRA I</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">Exercise #1</span></p> <ol> <li><span XXXXX="s1">True (b) XXXX (c) False (d) XXXX (e) True (f) True (g) XXXXX (h) True</span></li> </ol> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">XXXXXXXX #X</span></p> <p><span XXXXX="XX" <the="" XXXXXXXXX="" is="" true.="" 4="" XX="" more="" than="" -X="" (a="" XXXXXXXX="" XXXXXX="" always="" a="" negative="" number).="">span class="XXXXX-XXXXXXXXX-space"&XX;</span></p> <p><span XXXXX="XX"></span> </p> <ol> <li><span class="XX">XXXX</span></li> </ol> <p><span class="s1"></span> </p> <p><span XXXXX="s1">-X<span XXXXX="XXXXX-tab-span"> </span>-3<span XXXXX="XXXXX-tab-span"> </span>-X<span XXXXX="XXXXX-tab-span"> </span>-X<span XXXXX="Apple-tab-span"> </span>X<span XXXXX="Apple-tab-span"> </span>X<span XXXXX="XXXXX-tab-span"> </span>2<span class="Apple-tab-span"> </span>X</span></p> <p><span class="s1">XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX</span></p> <p><span class="XX"></span> </p> <p><span class="XX">(b) False</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">-X <span class="Apple-tab-span"> </span>-X<span class="XXXXX-tab-span"> </span>-3</span></p> <p><span class="s1">XXXXXXXXXXXXXXX</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">(c) XXXX</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">-6<span class="XXXXX-tab-span"> </span>-X<span class="Apple-tab-span"> </span>-4<span class="Apple-tab-span"> </span>-3<span XXXXX="XXXXX-tab-span"> </span>-2<span XXXXX="Apple-tab-span"> </span>-X<span XXXXX="XXXXX-tab-span"> </span>0</span></p> <p><span class="XX">XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">XXXXXXXX #4</span></p> <p><span class="XX">X(x - 2) ≥ 2x + 1</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">(a) X(XX - X) ≥ 2 (10) + 1</span></p> <p><span XXXXX="s1">XX ≥ 20 + X</span></p> <p><span class="XX">24 ≥ XX</span></p> <p><span class="XX">XXX inequality is XXXXX</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">(b) X(X - X) ≥ 2 (X) + 1</span></p> <p><span XXXXX="XX">9 ≥ 11</span></p> <p><span class="XX">The inequality is false</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">(c) 3(X - 2) ≥ X (X) + 1</span></p> <p><span XXXXX="s1">-X ≥ 3</span></p> <p><span class="XX">XXX inequality is XXXXX</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">(d) X(X - X) ≥ 2 (X) + 1</span></p> <p><span class="XX">15 ≥ 15</span></p> <p><span XXXXX="XX">XXX XXXXXXXXXX XX true</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">Exercise #X</span></p> <p><span class="XX">(a) 2x + 4 &XX; XX - 1</span></p> <p><span class="s1">x = 1</span></p> <p><span XXXXX="XX">X(X) + X &XX; X(X) - 1</span></p> <p><span class="XX">X &XX; X</span></p> <p><span class="XX">The inequality is XXXX</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">(b) -3 (x+5) ≥ </span><span class="XX">x+X</span></p> <p><span XXXXX="XX"><span class="Apple-tab-span"> </span><span XXXXX="XXXXX-tab-span"> </span>X<span XXXXX="Apple-tab-span"> </span><span class="XXXXX-tab-span"> </span>for x = -3</span></p> <p><span XXXXX="XX">-X (x + X) ≥ x + 7</span></p> <p><span XXXXX="XX">-X (-X + X) ≥ -X + 7</span></p> <p><span class="s1">-12 ≥ 4</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">The inequality XX false</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">(c) x</span><span class="XX"><XXX>X </sup></span><span XXXXX="XX">-10x + X &XX; XX + XX<span XXXXX="XXXXX-tab-span"> </span>XXX x = -X</span></p> <p><span class="XX">XXXXXXXXXX x = -2</span></p> <p><span class="XX">(-2)</span><span XXXXX="s4"><sup>2 </XXX></span><span class="s1">-XX(-2) + 1 < 20 + 5(-X)</span></p> <p><span XXXXX="XX">4 + 20 + 1 &XX; 20 - 10</span></p> <p><span XXXXX="s1">XX &XX; 10</span></p> <p><span class="s1"></span> </p> <p><span class="s1">The XXXXXXXXXX is false</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">(d) </span><span class="s2">2 (x - 5)</span><span class="s1"> + X ≤ </span><span XXXXX="XX">x - 2 </span><span class="s1"><span XXXXX="Apple-converted-XXXXX"> <span class="XXXXX-tab-span"> </span></span>for x = 5</span></p> <p><span class="s1"><span class="Apple-tab-span"> </span>3<span class="XXXXX-tab-span"> </span><span class="Apple-converted-space"> </span>X</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"> </span><span XXXXX="XX">X (5 - X)</span><span class="s1"> + 1 ≤ </span><span class="XX">X - X </span><span XXXXX="s1"><span XXXXX="XXXXX-converted-space"> <span class="XXXXX-tab-span"> </span></span>XXX x = 5</span></p> <p><span class="s1"><span class="Apple-tab-span"> </span>3<span class="Apple-tab-span"> </span><span class="XXXXX-converted-space"> </span>X</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"><span XXXXX="Apple-tab-span"> </span>0 + X ≤ 1/3</span></p> <p><span XXXXX="XX"><span class="XXXXX-tab-span"> </span><span class="Apple-converted-XXXXX"> </span>X ≤ X/X</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX" <the="" XXXXXXXXXX="" is="" XXXXX="">span class="XXXXX-converted-XXXXX"&XX;</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">INEQUALITIES COMMON XXXX XXXXXXX I XXXXXXXX</span></p> <p><span class="s1">XXXXXXX</span></p> <ol> <li><span class="s1">(a) True (b) XXXXX (c) False (d) True (e) XXXXX (f) XXXX (g)XXXX (h) XXXXX</span></li> </ol> <p><span XXXXX="s1">2. (a) 3x + X ≤ XX - X <span class="XXXXX-tab-span"> </span>for x = 8</span></p> <p><span XXXXX="s1"><span XXXXX="XXXXX-tab-span"> </span>X(8) + 2 ≤ 2(8) - 5</span></p> <p><span class="XX"><span XXXXX="XXXXX-tab-span"> </span>24 + 2 ≤ XX - X</span></p> <p><span XXXXX="XX"><span XXXXX="XXXXX-tab-span"> </span>26 ≤ XX</span></p> <p><span XXXXX="XX">The inequality XX false</span></p> <p><span class="XX"></span> </p> <p><span class="s1">(b)<span class="Apple-XXXXXXXXX-space"> </span>3x + X ≤ X - XX <span class="Apple-tab-span"> </span>for x = -X</span></p> <p><span class="s1"><span XXXXX="Apple-XXXXXXXXX-space"> </span>X(-2) + X ≤ X - X(-X)</span></p> <p><span XXXXX="s1"><span class="XXXXX-XXXXXXXXX-XXXXX"> </span>-X + X ≤ -X</span></p> <p><span class="s1">The inequality is true</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">(c) (x-3)</span><span XXXXX="XX"><sup>2 </sup></span><span class="s1">&XX; -3(x+2)<span XXXXX="XXXXX-tab-span"> </span>XXX x = 3</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">(3-X)</span><span XXXXX="XX"><sup>2 </XXX></span><span class="XX">> -X(3+X)</span></p> <p><span class="XX">X &XX; -15</span></p> <p><span class="s1">The XXXXXXXXXX XX true</span></p> <p><span class="s1"></span> </p> <p><span class="XX">(d) </span><span class="s2">2 (3-2x)</span><span XXXXX="XX"> ≤ 2x - X(x+1)<span XXXXX="Apple-tab-span"> </span>for x = -X</span></p> <p><span XXXXX="s1"><span class="XXXXX-tab-span"> </span>5</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">2 (X+X)</span><span class="XX"> ≤ -X - 3(X)<span XXXXX="Apple-tab-span"> </span>XXX x = -1</span></p> <p><span XXXXX="s1"><span class="XXXXX-XXXXXXXXX-space"> </span>5</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">12/5 ≤ -2</span></p> <p><span class="s1">XXX XXXXXXXXXX is false</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">(e) </span><span class="s2">3</span><span XXXXX="XX"><XXX>2</XXX></span><span XXXXX="XX"> - 4(X) + 9</span><span class="s1"> > </span><span XXXXX="s2">3(X) + X</span></p> <p><span class="XX"><span XXXXX="Apple-tab-span"> </span>6<span class="Apple-tab-span"> </span><span XXXXX="Apple-XXXXXXXXX-space"> </span>X<span class="XXXXX-tab-span"> </span><span XXXXX="XXXXX-tab-span"> </span><span class="Apple-tab-span"> </span>for x = X</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s2">X - XX + X</span><span class="s1"> > X</span><span XXXXX="s2"> + X</span></p> <p><span class="s1"><span class="XXXXX-converted-XXXXX"> </span>6<span class="Apple-tab-span"> </span><span class="XXXXX-converted-XXXXX"> </span>5<span XXXXX="Apple-tab-span"> </span><span class="XXXXX-tab-span"> </span><span class="Apple-tab-span"> </span>for x = 3</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s2">6</span><span class="XX"> > </span><span class="XX">XX</span></p> <p><span XXXXX="XX">X <span XXXXX="Apple-converted-space"> </span>5<span XXXXX="XXXXX-tab-span"> </span><span class="Apple-tab-span"> </span><span class="Apple-tab-span"> </span>for x = X</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">1 > 2 for x = X</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">XXX XXXXXXXXXX is false</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">| </span><span XXXXX="s2">-X (5 - x) </span><span class="XX">| ≥ </span><span class="XX">3x - X</span></p> <p><span XXXXX="s1"><span XXXXX="Apple-converted-space"> </span>X<span XXXXX="Apple-tab-span"> </span><span XXXXX="Apple-tab-span"> </span>2<span class="Apple-tab-span"> </span><span XXXXX="Apple-tab-span"> </span>for x = -X</span></p> <p><span class="XX"></span> </p> <p><span class="s1">| </span><span XXXXX="s2">-2 (X +1) </span><span class="s1">| ≥ </span><span XXXXX="s2">-3 - X</span></p> <p><span XXXXX="XX"><span class="Apple-converted-XXXXX"> </span>3<span XXXXX="XXXXX-tab-span"> </span><span XXXXX="XXXXX-tab-span"> </span>X<span class="Apple-tab-span"> </span><span class="Apple-tab-span"> </span>XXX x = -X</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">4 ≥ -X</span></p> <p><span XXXXX="s1">XXX inequality is XXXX</span></p> <p><span class="s1"></span> </p> <p><span class="XX"><b>Applications<span class="Apple-converted-space"></span></b></span></p> <p><span class="XX"><b>3.<span XXXXX="XXXXX-converted-space"></span></b></span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"><b>x = 12</b></span></p> <p><span class="s2">X(x + X) - 1</span><span XXXXX="XX"> + X (XX - X)<span XXXXX="Apple-converted-XXXXX"> </span>≤ 125</span></p> <p><span XXXXX="s1"><span XXXXX="Apple-XXXXXXXXX-space"> </span>2</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s2">3(XX + X) - X</span><span class="s1"> + 4 (2(XX) - X)<span XXXXX="Apple-converted-XXXXX"> </span>≤ 125</span></p> <p><span class="XX"><span class="XXXXX-XXXXXXXXX-XXXXX"> </span>2</span></p> <p><span class="XX"></span> </p> <p><span class="XX">50/X + 84 ≤ XXX</span></p> <p><span class="XX">XXX ≤ XXX</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">The inequality is XXXX. The machine is XXXX XX XXX XX pressure = XX</span></p> <p><span class="XX"></span> </p> <p><span class="XX"><b>x = 13</b></span></p> <p><span class="s1"></span> </p> <p><span class="XX">3(x + 5) - X</span><span class="XX"> + 4 (2x - X)<span XXXXX="Apple-XXXXXXXXX-space"> </span>≤ 125</span></p> <p><span XXXXX="s1"><span class="Apple-XXXXXXXXX-space"> </span>X</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">3(13 + 5) - 1</span><span XXXXX="s1"> + 4 (X(XX) - 3)<span class="XXXXX-converted-space"> </span>≤ XXX</span></p> <p><span XXXXX="XX"><span class="XXXXX-converted-XXXXX"> </span>2</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">XX/X + 92 ≤ 125</span></p> <p><span class="XX">118.X ≤ XXX</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">XXX XXXXXXXXXX XX XXXX. The XXXXXXX XX safe XX run XX pressure = XX</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="XX"><b>x = 14</b></span></p> <p><span class="s2">X(x + X) - 1</span><span XXXXX="XX"> + 4 (XX - X)<span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>≤ 125</span></p> <p><span XXXXX="XX"><span class="XXXXX-converted-space"> </span>2</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">X(XX + X) - X</span><span class="s1"> + X (2(14) - X)<span XXXXX="XXXXX-converted-space"> </span>≤ XXX</span></p> <p><span class="XX"><span XXXXX="XXXXX-XXXXXXXXX-space"> </span>X</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">XX + 100 ≤ XXX</span></p> <p><span XXXXX="s1">128 ≤ 125</span></p> <p><span XXXXX="XX">XXX XXXXXXXXXX is XXXXX. XXX machine XX unsafe XX XXX XX XXXXXXXX = 14</span></p> <p><span class="XX"></span> </p> <p><span class="s1">(b) x = X</span></p> <p><span class="XX">3(x + X) - X</span><span class="s1"> + 4 (2x - X)<span XXXXX="XXXXX-converted-space"> </span>&XX; XX</span></p> <p><span XXXXX="s1"><span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>2</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"></span> </p> <p><span class="s1"></span> </p> <p><span class="XX">3(5 + 5) - X</span><span XXXXX="XX"> + X (X(5) - X)<span XXXXX="Apple-XXXXXXXXX-space"> </span>&XX; 35</span></p> <p><span XXXXX="XX"><span class="Apple-XXXXXXXXX-XXXXX"> </span>X</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">XX.X + XX &XX; 35</span></p> <p><span class="XX">XX.X &XX; 35</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1" <the="" machine="" XXXX="" run="" XX="" the="" pressure="" is="" XXXXX="" 35="" pounds="" XXX="" square="" inch.="">span class="Apple-XXXXXXXXX-XXXXX"&XX;</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">XXXXXXXXX</span></p> <p><span class="s1">4. (a) 4(-2) + X &XX; X - 3(-X)</span></p> <p><span XXXXX="s1"><span class="Apple-tab-span"> </span>-X &XX; X</span></p> <p><span class="XX" <XXX="" XXXXXXX="" sign="" is="" &XX;="">span XXXXX="Apple-XXXXXXXXX-XXXXX"></span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">(b) (2x + 1)/ (-X) < 4 / (2-3x)</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">(X(-2) + X)/ (-X) &XX; X / (2-X(-2))</span></p> <p><span class="s1">1 &XX; 4/X</span></p> <p><span class="XX">1 > X/X</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">XXX correct sign XX &XX;</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">(c) 2x</span><span class="XX"><XXX>X </XXX></span><span class="XX">+X &XX; |X - XX|</span></p> <p><span XXXXX="s1">2(X)</span><span class="XX"><sup>X </XXX></span><span class="XX">+5 > |1 - 9(4)|</span></p> <p><span XXXXX="s1">37 &XX; 35</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">XXX correct XXXX is ></span></p> <p><span class="s1"></span> </p> <p><span class="s1">(d) ((3(2x - 5)) / 3) + 2 <span XXXXX="Apple-tab-span"> </span>&XX; 8(3(x) - X)</span></p> <p><span class="XX">((3(X(X) - 5)) / X) + X <span XXXXX="Apple-tab-span"> </span>< X(X(X) - 6)</span></p> <p><span class="XX">7 < 72</span></p> <p><span class="s1"></span> </p> <p><span class="XX">The XXXXXXX XXXX XX <</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="XX"></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 XXXXX="s1"></span> </p> <p><span class="s1"></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="s1"></span> </p> <p><span class="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="XX"></span> </p> <p><span XXXXX="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 class="XX"></span> </p> <p><span XXXXX="s1">XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX</span></p> <p><span XXXXX="s1">EQUATIONS AND XXXXX XXXXXXXXX XXXXXX XXXX ALGEBRA I</span></p> <p><span class="s1"></span> </p> <p><span class="XX">XXXXXXXX #1</span></p> <p><span XXXXX="XX">(X) X(4x + X)<span XXXXX="XXXXX-converted-XXXXX"> </span>is not an equation.</span></p> <p><span class="XX">XXX other three options are XXXXXXXXX as XXXX are in XXX equation format.</span></p> <p><span class="s1"></span> </p> <p><span class="s1">XXXXXXXX #X</span></p> <p><span class="XX">(a) XX cannot XXXXXXXXX XXXXXXX XX - 8 = 10 - x is true or XXXXX XX we XX not XXXX the value of XXX unknowns, and hence we do XXX XXXX if the equation XXXXX.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">(b) If x = 5, XXX XXXXXXXX evaluates XX 10 - X = XX - 5 &XX;&XX;&XX; X = 5. XXX equation XXXX be XXXXX.</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">(c) XX - 8 = 10 - x</span></p> <p><span class="s1">X(X) - X = XX - X</span></p> <p><span class="XX">4 = X</span></p> <p><span class="XX" <the="" XXXXXXXX="" is="" XXXX="" XX="" XXXX="" XXXXX="" hold.="">span XXXXX="Apple-XXXXXXXXX-space"&XX;</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">XXXXXXXX #X</span></p> <p><span XXXXX="s1">(a)<span XXXXX="XXXXX-converted-XXXXX"> </span>XX + 3 = XX</span></p> <p><span XXXXX="XX">2(X) + 3 = 17</span></p> <p><span XXXXX="XX">17 = XX</span></p> <p><span class="s1">XXX XXXXXXXX is true.</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">(b) </span><span class="s2">(x - 20)</span><span XXXXX="s1"> = -4</span></p> <p><span class="XX"><span XXXXX="XXXXX-XXXXXXXXX-space"> </span>X</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s2">(XX - XX)</span><span class="XX"> = -4</span></p> <p><span XXXXX="s1"><span XXXXX="XXXXX-converted-space"> </span>X</span></p> <p><span class="s1"></span> </p> <p><span class="s2">(-10)</span><span XXXXX="s1"> = -4</span></p> <p><span XXXXX="s1"><span XXXXX="XXXXX-XXXXXXXXX-space"> </span>5</span></p> <p><span class="XX"></span> </p> <p><span class="XX">-X = -X</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">The XXXXXXXX is false</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">(c) X (x+X) = 6 (x - 1)<span class="XXXXX-converted-space"></span></span></p> <p><span class="s1">X (4 + 5) = 6 ( 4 - 1)</span></p> <p><span XXXXX="s1">18 = XX</span></p> <p><span class="XX"></span> </p> <p><span class="s1">XXX XXXXXXXX is true</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">(d)<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"></span></span></p> <p><span class="s1">x</span><span class="XX"><sup>2 </sup></span><span XXXXX="s1">-X</span><span class="XX"> </span><span class="XX">= 2x + X</span></p> <p><span class="XX">(-X)</span><span class="XX"><sup>X </XXX></span><span class="XX">-X</span><span class="s4"> </span><span class="s1">= 2(-X) + 2</span></p> <p><span class="s1">X -X = 2 - X</span></p> <p><span XXXXX="XX">0 = X</span></p> <p><span XXXXX="s1">The XXXXXXXX is true</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">(e) </span><span class="s2">X (x + 2)</span><span class="XX"> - X = 5</span></p> <p><span XXXXX="XX"><span XXXXX="Apple-tab-span"> </span>4</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">3 ((X) + X)</span><span class="XX"> - 1 = 5</span></p> <p><span class="s1"><span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>4</span></p> <p><span class="s1"></span> </p> <p><span class="XX">12 - X = XX</span></p> <p><span XXXXX="s1">8 = XX</span></p> <p><span XXXXX="XX">XXX equation XX false</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">(f) X/X x - X = -1/X x + 9</span></p> <p><span class="s1">X/X (8) - X = -1/X (8) + X</span></p> <p><span XXXXX="XX">6 - X = X - X</span></p> <p><span XXXXX="XX">5 = X</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">The equation XX true</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">XXXXXXXX #X</span></p> <p><span class="XX">XX - 3 = X x + 11</span></p> <p><span class="XX">4(X) - 3 = X(7) + 11</span></p> <p><span class="XX">XX = XX</span></p> <p><span class="s1">It is correct as a XXXXXXXX.</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">XXXX’s XXXXX was to complete XXX XXXXXXXXXX X-X XXX X + 11 before XXX operations 4(X) and 2(X).</span></p> <p><span XXXXX="XX">XXXXXXXXXXXXXX should always come before addition XXX XXXXXXXXXXX.</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">XXXXXXX</span></p> <p><span class="XX">1. (a) Expression (b) Equation (c) XXXXXXXX (d) Expression (e) Expression (f) XXXXXXXX</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">2. (a) x - 4 = XX<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"></span></span></p> <p><span class="s1">X - 4 = 12<span XXXXX="XXXXX-XXXXXXXXX-space"></span></span></p> <p><span class="XX">X = 12</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">(b) (X+x) / X = 3</span></p> <p><span class="s1">(X+X) / 4 = X</span></p> <p><span class="XX">XX/4 = X</span></p> <p><span class="XX">XXX equation is XXXX. The solution is valid for the given equation.</span></p> <p><span class="XX"></span> </p> <p><span class="s1">(c) (x + X) - X(x-4) = X</span></p> <p><span class="XX">(X + 2) - 3(4-4) = X</span></p> <p><span class="XX">6 - 3(X) = 6</span></p> <p><span class="XX">6 = X</span></p> <p><span XXXXX="XX">XXX equation XX XXXX. XXX solution is XXXXX XXX XXX XXXXX XXXXXXXX.</span></p> <p><span class="s1"></span> </p> <p><span class="s1">(d) X/3 (x+X) = - 2/5 (x-9)</span></p> <p><span XXXXX="XX">X/3 (X+X) = - 2/X (X-9)</span></p> <p><span XXXXX="s1">2 = X</span></p> <p><span class="s1"></span> </p> <p><span class="s1">XXX XXXXXXXX is XXXX. The solution XX valid XXX the given equation.</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">Applications</span></p> <p><span class="s1">3.<span class="Apple-converted-space"></span></span></p> <p><span class="s1">XXX 1: X = X(X) + X = 11</span></p> <p><span XXXXX="XX">XXX 2: P = X(X) + 5 = XX</span></p> <p><span class="XX">Day 3: P = X(3) + X = XX</span></p> <p><span XXXXX="XX">XXX 4: P = 6(4) + 5 = 29</span></p> <p><span class="XX">Day 5: P = X(X) + 5 = XX</span></p> <p><span class="XX">Day X: X = 6(X) + 5 = XX</span></p> <p><span XXXXX="s1">XXX X: X = X(7) + 5 = XX</span></p> <p><span class="s1">Day 8: P = X(8) + 5 = 53</span></p> <p><span XXXXX="XX">We will XXXXXXX XXXXX 1 on XXX X, XXXXX X on XXX 2 to X, Stage X XXX XXX X XX X, and incurable XXXXX on Day 8.<span class="Apple-converted-space"></span></span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">XXXXXXXXX</span></p> <p><span class="s1">X. 25w + XX = 250</span></p> <p><span class="s1">(a) XXXXXXX XXXXX 9 weeks = 25 (9) + 30 = 255</span></p> <p><span class="XX">Yes, bobby will have enough as 255 > 250</span></p> <p><span class="XX">(b) XXX + 30 + XXX = 250 + XXX</span></p> <p><span class="XX">XXXXX 9 XXXXX XX saving = 25(X) + 30 + 10(9) = 345</span></p> <p><span class="s1">XXXXX needs 250 + XXX = XXX</span></p> <p><span XXXXX="s1">Nine XXXXX XX XXX enough XXXX for XXXXX to XXXX XX XXX < XXX</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 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 class="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></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 XXXXX="XX"></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 class="XX"></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 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 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 XXXXX="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="s1"></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 class="XX"></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="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">527CCAlg1U2L9SolvingLinearInequalities</span></p> <p><span XXXXX="XX">SOLVING XXXXXX XXXXXXXXXXXX COMMON XXXX XXXXXXX I</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">Exercise #X</span></p> <p><span class="XX">(a) XXX XXX inequality is X &XX; 11. XXXX is a true inequality.</span></p> <p><span XXXXX="XX">(b) The new XXXXXXXXXX XX 0 < X. XXXX XX a true XXXXXXXXXX.</span></p> <p><span class="XX">(c) The XXX XXXXXXXXXX XX X &XX; 16. This XX a XXXX XXXXXXXXXX.</span></p> <p><span XXXXX="XX">(d) The new inequality XX X &XX; 4. XXXX is a XXXX inequality.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">Exercise #2</span></p> <p><span class="s1">(a) The new inequality is -8 &XX; -16. This is a XXXXX inequality.</span></p> <p><span class="s1">(a) XXX new inequality is -2 &XX; -4. XXXX XX a XXXXX XXXXXXXXXX.</span></p> <p><span class="s1"></span> </p> <p><span class="s1">Exercise #X</span></p> <p><span class="XX">(a) XXX inequality XX 5 < 8. When multiplied by -4, it XXXXXXX -20 &XX; -32. This becomes false.<span class="Apple-XXXXXXXXX-space"></span></span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">Exercise #4</span></p> <p><span class="XX">(a) 4x - 3 ≥ 5</span></p> <p><span class="s1">4x ≥ 8</span></p> <p><span XXXXX="XX">x ≥ X</span></p> <p><span class="s1"></span> </p> <p><span class="XX">(b) / (c)</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">XXX five XXXXXXX are X, 4, X, X, 7</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">XXX solution XX XXXXXXXXX XX XXX XXXXX >>>&XX;&XX;>&XX;>&XX;</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"><span XXXXX="Apple-tab-span"> </span><span XXXXX="XXXXX-tab-span"> </span><span class="Apple-tab-span"> </span><span class="XXXXX-tab-span"> </span><span class="Apple-tab-span"> </span><span class="XXXXX-tab-span"> </span> <span XXXXX="Apple-converted-space"> </span>>>&XX;&XX;>>>&XX;&XX;>&XX;>&XX;>&XX;&XX;>&XX;>>&XX;&XX;>>>>>&XX;>&XX;>&XX;</span></p> <p><span XXXXX="s1">-XX<span class="XXXXX-converted-space"> </span>-9<span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>-8 <span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>-X<span class="XXXXX-converted-space"> </span>-X <span XXXXX="XXXXX-XXXXXXXXX-space"> </span>-5 <span XXXXX="Apple-converted-XXXXX"> </span>-4<span class="Apple-XXXXXXXXX-XXXXX"> </span>-X <span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>-2 <span XXXXX="XXXXX-converted-XXXXX"> </span>-X<span class="Apple-converted-space"> </span>X<span class="XXXXX-converted-XXXXX"> </span>X <span XXXXX="XXXXX-converted-space"> </span>X <span class="Apple-XXXXXXXXX-space"> </span>3<span class="XXXXX-XXXXXXXXX-space"> </span>4<span XXXXX="XXXXX-converted-XXXXX"> </span>5<span XXXXX="XXXXX-converted-XXXXX"> </span>6<span XXXXX="XXXXX-converted-XXXXX"> </span>X<span class="XXXXX-XXXXXXXXX-space"> </span>8<span class="Apple-converted-space"> </span>X<span class="XXXXX-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 XXXXX="s1"></span> </p> <p><span class="XX">Exercise #X<span class="XXXXX-converted-space"></span></span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">(a) Rewrite the left hand expression as an XXXXXXXXXX XXXXXXXXXX using addition.</span></p> <p><span class="XX">8 - XX > 16</span></p> <p><span class="s1">8 - XX &XX; XX</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">(b) XXXXX the XXXXXXXXXX</span></p> <p><span XXXXX="s1">X - XX > XX</span></p> <p><span class="XX">X - XX &XX; 2x</span></p> <p><span XXXXX="XX">-X &XX; XX</span></p> <p><span XXXXX="XX">-X &XX; x</span></p> <p><span XXXXX="XX">x < -X</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">(c) Let x = -6</span></p> <p><span XXXXX="XX">XX -X < -4, XXX XXXXXXXX XXXXXXXXXX XX true</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">(d)<span XXXXX="XXXXX-converted-space"></span></span></p> <p><span class="s1">The XXXXXXXX XX XXXXXXXXX XX the range &XX;&XX;&XX;>>>&XX;>&XX;</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">&XX;&XX;<<&XX;&XX;<&XX;<&XX;&XX;&XX;&XX;<<<<<&XX;&XX;&XX;&XX;<</span></p> <p><span XXXXX="XX">-XX<span class="Apple-converted-space"> </span>-X<span XXXXX="XXXXX-converted-space"> </span>-X <span XXXXX="Apple-XXXXXXXXX-space"> </span>-7<span class="Apple-XXXXXXXXX-XXXXX"> </span>-6 <span XXXXX="Apple-converted-space"> </span>-X <span class="Apple-converted-XXXXX"> </span>-4<span class="XXXXX-XXXXXXXXX-space"> </span>-X <span class="XXXXX-converted-XXXXX"> </span>-2 <span class="Apple-converted-space"> </span>-1<span XXXXX="Apple-converted-XXXXX"> </span>X<span XXXXX="Apple-converted-XXXXX"> </span>1 <span XXXXX="Apple-converted-XXXXX"> </span>2 <span class="Apple-converted-space"> </span>X<span XXXXX="Apple-converted-XXXXX"> </span>4<span XXXXX="Apple-converted-XXXXX"> </span>X<span class="Apple-converted-space"> </span>6<span class="Apple-XXXXXXXXX-space"> </span>7<span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>X<span XXXXX="Apple-converted-XXXXX"> </span>X<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>10</span></p> <p><span class="XX">|XXXX|____|XXXX|____|XXXX|XXXX|XXXX|____|____|XXXX|XXXX|XXXX|____|____|XXXX|____|XXXX|XXXX|XXXX|XXXX|</span></p> <p><span class="s1"></span> </p> <p><span class="XX">XXXXXXXX #X<span class="XXXXX-XXXXXXXXX-XXXXX"></span></span></p> <p><span class="s1">(a)</span></p> <p><span class="s1">8 (x-2) - X (XX + X) ≤ XX + 4 - X(x+1)</span></p> <p><span XXXXX="s1">XX - 16 - 6x - X ≤ 7x + X - XX - 3</span></p> <p><span class="s1">XX - 19 ≤ XX + 1</span></p> <p><span XXXXX="s1">-XX ≤ 20</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">(b)<span XXXXX="Apple-converted-XXXXX"></span></span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">8 (x-X) - 3 (XX + X) ≤ XX + X - 3(x+X)</span></p> <p><span XXXXX="XX">XX - XX - XX - 3 ≤ XX + X - XX - 3</span></p> <p><span class="XX">XX - XX ≤ XX + X</span></p> <p><span class="XX">-2x ≤ 20</span></p> <p><span class="XX">-x ≤ 10</span></p> <p><span XXXXX="s1">x ≥ -10</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"><span XXXXX="XXXXX-tab-span"> </span><span XXXXX="Apple-tab-span"> </span><span class="Apple-tab-span"> </span> <span class="XXXXX-XXXXXXXXX-XXXXX"> </span>O>&XX;&XX;>&XX;>>>>>>&XX;>>&XX;&XX;>>>>>&XX;>&XX;&XX;>>>&XX;&XX;</span></p> <p><span XXXXX="s1">-16 -XX -14- <span XXXXX="Apple-converted-XXXXX"> </span>13 -12<span class="Apple-XXXXXXXXX-XXXXX"> </span>-XX <span class="Apple-XXXXXXXXX-space"> </span>-XX<span class="Apple-XXXXXXXXX-XXXXX"> </span>-9<span class="Apple-converted-space"> </span>-X <span class="Apple-converted-XXXXX"> </span>-7<span XXXXX="XXXXX-XXXXXXXXX-space"> </span>-6 <span XXXXX="Apple-converted-XXXXX"> </span>-5 <span class="XXXXX-XXXXXXXXX-XXXXX"> </span>-4<span class="Apple-XXXXXXXXX-XXXXX"> </span>-X <span class="Apple-converted-XXXXX"> </span>-2 <span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>-X<span class="XXXXX-XXXXXXXXX-XXXXX"> </span>0</span></p> <p><span class="XX">|____|XXXX|____|XXXX|XXXX|____|XXXX|XXXX|XXXX|____||____|____|XXXX|____|XXXX|XXXX|</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">XXXXXXX</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">(a)<span class="Apple-XXXXXXXXX-XXXXX"></span></span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">5x - X ≤ 24</span></p> <p><span class="XX">5x ≤ XX</span></p> <p><span class="s1">x ≤ 6</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="XX">XXX solution XX XXXXXXXXX XX XXX XXXXX >&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;<<<<&XX;&XX;<<&XX;<&XX;<&XX;&XX;&XX;&XX;<<<<&XX;&XX;&XX;&XX;<&XX;<&XX;<<<&XX;&XX;X</span></p> <p><span class="s1">-10<span class="Apple-converted-space"> </span>-X<span XXXXX="XXXXX-XXXXXXXXX-space"> </span>-8 <span class="Apple-converted-XXXXX"> </span>-X<span class="XXXXX-XXXXXXXXX-space"> </span>-6 <span class="Apple-XXXXXXXXX-XXXXX"> </span>-X <span class="XXXXX-XXXXXXXXX-space"> </span>-X<span class="Apple-converted-XXXXX"> </span>-3 <span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>-X <span class="XXXXX-XXXXXXXXX-space"> </span>-X<span class="Apple-converted-XXXXX"> </span>X<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>X <span XXXXX="Apple-XXXXXXXXX-space"> </span>X <span class="Apple-XXXXXXXXX-space"> </span>3<span class="Apple-XXXXXXXXX-space"> </span>X<span class="XXXXX-XXXXXXXXX-XXXXX"> </span>5<span class="XXXXX-XXXXXXXXX-space"> </span>6<span class="Apple-converted-XXXXX"> </span>7<span class="XXXXX-converted-XXXXX"> </span>8<span XXXXX="Apple-XXXXXXXXX-space"> </span>X<span class="XXXXX-XXXXXXXXX-space"> </span>XX</span></p> <p><span XXXXX="s1">|____|XXXX|____|XXXX|XXXX|____|____|____|XXXX|XXXX|____|____|XXXX|____|____|____|____|XXXX|____|XXXX|</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">(b)</span></p> <p><span class="s1"></span> </p> <p><span class="s1">2(5-x) ≤ 12</span></p> <p><span class="s1">XX - 2x ≤ XX</span></p> <p><span XXXXX="s1">XX - 12 ≤ 2x</span></p> <p><span XXXXX="s1">-2 ≤ 2x</span></p> <p><span class="XX">-X ≤ x</span></p> <p><span class="s1"></span> </p> <p><span class="XX">XXX solution XX XXXXXXXXX by the XXXXX &XX;>&XX;&XX;&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;<O</span></p> <p><span class="s1">-XX<span class="Apple-XXXXXXXXX-space"> </span>-X<span XXXXX="Apple-XXXXXXXXX-space"> </span>-8 <span XXXXX="Apple-converted-XXXXX"> </span>-7<span class="XXXXX-converted-space"> </span>-6 <span class="XXXXX-converted-XXXXX"> </span>-5 <span class="Apple-converted-XXXXX"> </span>-4<span class="XXXXX-XXXXXXXXX-space"> </span>-X <span XXXXX="XXXXX-converted-XXXXX"> </span>-X <span XXXXX="XXXXX-converted-space"> </span>-X<span class="XXXXX-converted-XXXXX"> </span>0<span class="Apple-converted-space"> </span>X <span class="Apple-XXXXXXXXX-space"> </span>2 <span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>3<span class="Apple-XXXXXXXXX-space"> </span>X<span XXXXX="Apple-converted-XXXXX"> </span>5<span XXXXX="XXXXX-converted-XXXXX"> </span>6<span class="Apple-XXXXXXXXX-space"> </span>7<span XXXXX="XXXXX-converted-space"> </span>8<span class="Apple-XXXXXXXXX-XXXXX"> </span>X<span XXXXX="Apple-converted-space"> </span>XX</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 class="s1">(c)</span></p> <p><span XXXXX="s1">X - 4x > XX</span></p> <p><span XXXXX="XX">-4x &XX; 12</span></p> <p><span XXXXX="s1">x &XX; XX/-4</span></p> <p><span class="s1">x &XX; -3</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">XXX XXXXXXXX is indicated by the XXXXX &XX;&XX;&XX;>>&XX;>&XX;&XX;</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1"><<&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 XXXXX="XXXXX-converted-space"> </span>-X <span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>-7<span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>-X <span class="XXXXX-XXXXXXXXX-space"> </span>-X <span class="XXXXX-converted-XXXXX"> </span>-4<span class="XXXXX-XXXXXXXXX-XXXXX"> </span>-X <span class="XXXXX-converted-XXXXX"> </span>-X <span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>-1<span class="XXXXX-converted-space"> </span>0<span XXXXX="XXXXX-converted-space"> </span>1 <span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>2 <span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>X<span XXXXX="XXXXX-converted-space"> </span>4<span XXXXX="XXXXX-converted-XXXXX"> </span>5<span XXXXX="XXXXX-XXXXXXXXX-space"> </span>X<span class="Apple-converted-XXXXX"> </span>7<span class="XXXXX-converted-space"> </span>X<span class="Apple-converted-space"> </span>X<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>10</span></p> <p><span class="XX">|XXXX|____|____|XXXX|____|____|XXXX|____|____|XXXX|____|XXXX|XXXX|____|XXXX|XXXX|XXXX|XXXX|____|____|</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">(d)</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">XX - X(x-2) > XX - 2x</span></p> <p><span XXXXX="XX">8x - XX + 12 > 20 - 2x</span></p> <p><span class="XX">XX + XX > XX - 2x</span></p> <p><span class="XX">XX > XX - XX</span></p> <p><span class="s1">XX > X</span></p> <p><span XXXXX="s1">x &XX; X</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"><span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>>&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>-X<span XXXXX="Apple-XXXXXXXXX-space"> </span>-8 <span class="XXXXX-XXXXXXXXX-space"> </span>-7<span XXXXX="XXXXX-XXXXXXXXX-space"> </span>-6 <span class="XXXXX-XXXXXXXXX-space"> </span>-5 <span XXXXX="XXXXX-converted-space"> </span>-X<span XXXXX="XXXXX-converted-XXXXX"> </span>-3 <span class="Apple-XXXXXXXXX-XXXXX"> </span>-X <span class="Apple-XXXXXXXXX-XXXXX"> </span>-X<span XXXXX="Apple-XXXXXXXXX-space"> </span>0<span class="Apple-converted-space"> </span>1 <span class="XXXXX-converted-space"> </span>2 <span XXXXX="Apple-converted-space"> </span>3<span class="Apple-converted-XXXXX"> </span>X<span class="Apple-converted-space"> </span>X<span class="XXXXX-XXXXXXXXX-space"> </span>X<span XXXXX="XXXXX-converted-space"> </span>7<span XXXXX="XXXXX-XXXXXXXXX-space"> </span>X<span XXXXX="Apple-converted-XXXXX"> </span>X<span class="Apple-XXXXXXXXX-XXXXX"> </span>XX</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 class="s1"></span> </p> <p><span class="XX">X (XX + X)</span><span class="XX"> > </span><span class="XX">X </span><span class="s1">x + X</span></p> <p><span XXXXX="s1"><span class="XXXXX-XXXXXXXXX-space"> </span>6 <span class="XXXXX-converted-XXXXX"> </span>X</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">X (XX + 2) &XX; 2x + 12</span></p> <p><span XXXXX="s1">XX + X &XX; XX + 12</span></p> <p><span XXXXX="XX">4x &XX; 6</span></p> <p><span class="XX">x &XX; X.5</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1"><span XXXXX="XXXXX-XXXXXXXXX-space"> </span>>&XX;>&XX;&XX;&XX;>>>>>&XX;&XX;>>&XX;>&XX;>&XX;&XX;&XX;&XX;&XX;>>></span></p> <p><span class="s1">-10<span XXXXX="XXXXX-converted-XXXXX"> </span>-9<span class="Apple-XXXXXXXXX-space"> </span>-X <span class="Apple-converted-XXXXX"> </span>-7<span XXXXX="Apple-XXXXXXXXX-space"> </span>-6 <span class="Apple-converted-space"> </span>-X <span XXXXX="Apple-XXXXXXXXX-space"> </span>-X<span class="Apple-converted-space"> </span>-X <span class="Apple-XXXXXXXXX-XXXXX"> </span>-2 <span XXXXX="Apple-XXXXXXXXX-space"> </span>-1<span class="XXXXX-converted-space"> </span>X<span XXXXX="XXXXX-converted-XXXXX"> </span>1 <span XXXXX="XXXXX-XXXXXXXXX-space"> </span>X <span XXXXX="Apple-XXXXXXXXX-space"> </span>X<span class="XXXXX-XXXXXXXXX-space"> </span>4<span XXXXX="XXXXX-converted-space"> </span>X<span XXXXX="Apple-converted-XXXXX"> </span>X<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>X<span class="Apple-XXXXXXXXX-space"> </span>8<span class="XXXXX-converted-XXXXX"> </span>9<span class="XXXXX-converted-XXXXX"> </span>XX</span></p> <p><span XXXXX="XX">|XXXX|XXXX|____|XXXX|XXXX|XXXX|XXXX|____|____|XXXX|XXXX|____|XXXX|XXXX|____|____|XXXX|____|XXXX|XXXX|</span></p> <p><span class="XX"></span> </p> <p><span class="XX">XXXXXXXXXXXX</span></p> <p><span class="XX">2. (a)<span XXXXX="XXXXX-converted-XXXXX"></span></span></p> <p><span XXXXX="s1">Edwin will XXX 45 + X.25n</span></p> <p><span XXXXX="s1">Edwin will pay more than XXXX if:</span></p> <p><span class="XX">45 + X.25n &XX; XXX</span></p> <p><span XXXXX="s1">XXXXXXX the inequality:</span></p> <p><span XXXXX="s1">5.25n > XXX - XX</span></p> <p><span class="XX">5.25n &XX; XX</span></p> <p><span class="XX">n > 12</span></p> <p><span class="s1"></span> </p> <p><span class="s1">(b)<span class="Apple-XXXXXXXXX-space"></span></span></p> <p><span class="XX">Edwin can XXXX 11 XXXXX and still pay XXXX than XXXX. This XX XXXXXXX 12 XXXX make XXXX XXXXX, and 13 or XXXXX will XXXX XXXXX XX XXX more than XXXX.</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="XX">XXXXXXXXX</span></p> <p><span XXXXX="XX">3. (a) XX + b ≥ XX</span></p> <p><span XXXXX="XX">ax ≥ XX - b</span></p> <p><span XXXXX="XX">x ≥ (cd - b) / a</span></p> <p><span class="s1"></span> </p> <p><span class="s1">(b)<span class="XXXXX-converted-space"></span></span></p> <p><span XXXXX="XX">a (x + 2) </span><span XXXXX="s1">&XX; c</span></p> <p><span class="s1"><span XXXXX="XXXXX-converted-XXXXX"> </span>b <span XXXXX="XXXXX-converted-space"></span></span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">ax + XX > bc</span></p> <p><span class="s1">x > </span><span XXXXX="XX">bc - XX<span XXXXX="XXXXX-converted-XXXXX"></span></span></p> <p><span XXXXX="s1"><span class="XXXXX-converted-space"> </span>a<span class="XXXXX-XXXXXXXXX-space"></span></span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">X. The XXXXXXX XXXXXX is (X)<span class="Apple-converted-XXXXX"></span></span></p> <p><span class="s1">ax + b > d</span></p> <p><span XXXXX="XX">x &XX; (d - b) /a</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="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="s1">97150</span></p> <p><span class="XX">XXXXXXXX 4: XXXXXX Day XXXXXXXXXXXXXXX/Dictatorship: A XXXXX of North Korea<span XXXXX="Apple-XXXXXXXXX-space"></span></span></p> <p><span class="XX">What historical XXXXXXX XXX you provide XX XXX XXXXX XXXXXX Government XXXX XX associated with XXX enduring issue you XXXXX?</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1" <the="" XXXXXXXX="" issue="" that="" most="" XXXXXXXXX="" me="" XX="" the="" XX="" XXXXX="" XXXXXX.="" XXXXXXXXX="" XX="" XX,="" XXXXXX="" are="" belong="" XXX="" XXXXXX,="" XXXXXXXXXX="" their="" gender,="" XXXXXX="" origin,="" ethnic="" XXXXXXXX,="" linguistic="" XXXXXXXXXX,="" XXXXX="" or="" other="" demographic="" XXXXXXXXXXX.="" these="" include="" XXXXX="" life="" and="" freedom,="" freedom="" from="" XXXXXXX="" XXXXXXXXXXX,="" XXXXXXX="" views,="" XXXXX="" XXXX="" for="" a="" fair="" wage,="" so="" on.="" north="" XXXXX’s="" historical="" context="" grim,="" its="" XXXXXX="" dismal.="" passage,="" 2014="" un="" commission="" inquiry="" found="" XXXXXXXXXX="" XXXXXXXXX="" gross,="" XXXXXXXXXX="" XXXXXXXXXX="" XXXXXX,="" XXXXXXXXX="" extermination,="" torture,="" XXXX="" XXXXXXXXXXXX.="">span class="XXXXX-converted-space"></span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX">XXXXX XXXXX XXX XXXXXX out of the repressive government of Kim Il-Sung, a post-XXX nationalist communist XXX XXXXXXXXX the XXXXX XXXXXXXXX of XXX XXXXX XXXXXX people in order XX deal XXXX XXXXXXXX emergencies XXXX as the Korean XXX. XXXXXXXXXXX, XXX Il-XXXX and XXX descendants have continued XX XXXXXXXXXXX power in a XXX XXXX curtails human XXXXXX in XXXXX XXXXX. They have XXXXXXX a regime XXXXX XXXX speech is disallowed, and where judicial penalties routinely XXXXX human XXXXXX. XXXXX XXXXXXX the use of torture, XXXXXX labor XXX XXXXXXXXXXXXX in XXXXXXXX XXXXXXXXXX. There is also XX XXXXXXXXXXX XXX process XXXXXX XXX judicial system. XXX lack XX human XXXXXX in XXXXX Korea XX a result XX decades XX XXXXXXXXXXXXX by the North Korean communist XXXXXXXXXXXX, in a bid to continue their firm grip on power over the XXXXXXX.<span class="Apple-XXXXXXXXX-space"></span></span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">XXX XXXX XXX issue of power/human rights in XXX government of North XXXXX XXXXXX XXXXXX?</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX" <XXX="" XXXXX="" korean="" people="" XXX="" XXXXXXXX="" in="" three="" main="" ways:="" XXXXXX,="" inhumane="" imprisonment="" and="" forced="" labor.="" XXXXXXXX,="" chronic="" XXXXXXXXXXXXX="" XX="" XXX="" economy="" XXX="" led="" to="" XXXXXXXXXX="" XXXXXXXX="" famines="" XXXX="" their="" XXXXXXXX.="" XXXX="" XXXXXXXX="" XXXX="" XXXXXXX="" work="" live.="" furthermore,="" koreans="" unable="" XXXXXX="" free="" XXXXX="" XXXX="" as="" XXX="" york="" times,="" XXXXX="" XXXXXX="" right="" speech.="" XXXX="" XXX="" move,="" XXXX="" movement="" limited="" XXXXXX="" restrictive="" XXXXX="" through="" border="" XXXXXXXX="" military="" checkpoints.="" XXXXXXX,="" political="" prisoners="" XXXXXXXXX="" have="" human="" rights="" violated="" labor,="" torture,="" under="" conditions.="" XXXXX="" XXXXXXX,="" korea="" XXXXXXXX="" XXXXXXXXX="" prison="" camps="" XXXXX="" perceived="" opponents="" XXXXXXXXXX="" sent="" XXXX="" starvation="" XXXXXXX="">span XXXXX="XXXXX-converted-space"&XX;</span></p> <p><span class="s1">94233</span></p> <p><span XXXXX="s1">Regular equations</span></p> <p><span class="XX">XX. x - 7 = X</span></p> <p><span class="XX">x = X + X</span></p> <p><span class="XX">x = XX</span></p> <p><span XXXXX="XX"></span> </p> <p><span class="s1">1b. x - b = a</span></p> <p><span class="XX">x = a + b</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">2a.<span XXXXX="XXXXX-XXXXXXXXX-XXXXX"> </span>4x = -12</span></p> <p><span XXXXX="XX">x = -X</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">XX. -XX = m</span></p> <p><span XXXXX="XX">k = m/(-X)<span class="Apple-XXXXXXXXX-XXXXX"></span></span></p> <p><span XXXXX="s1">X = </span><span XXXXX="s2">-X <span class="Apple-XXXXXXXXX-XXXXX"></span></span><span XXXXX="s1"> m</span></p> <p><span XXXXX="XX"><span class="Apple-XXXXXXXXX-space"> </span>3</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="XX">XX. XX - 5 = 11</span></p> <p><span class="XX"><span XXXXX="XXXXX-XXXXXXXXX-space"> </span>x = (XX + 5)/X = 8</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1">XX. 2b - 9 = d</span></p> <p><span XXXXX="s1"><span XXXXX="Apple-XXXXXXXXX-space"> </span>b = (d + X) / X</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">XX. 1/X<span XXXXX="Apple-converted-space"> </span>(4x) = -XX</span></p> <p><span class="s1"><span class="Apple-converted-space"> </span>XX = -40</span></p> <p><span XXXXX="XX"><span class="Apple-XXXXXXXXX-XXXXX"> </span>x = -XX</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">XX. XXX = 10</span></p> <p><span class="s1"><span class="XXXXX-XXXXXXXXX-space"> </span>g = 10 / XX</span></p> <p><span XXXXX="s1"></span> </p> <p><span XXXXX="s1">XX. x / -8 = 11</span></p> <p><span class="s1"><span XXXXX="Apple-XXXXXXXXX-XXXXX"> </span>x = - XX</span></p> <p><span class="s1"></span></p> <p><span XXXXX="s1">XX. y/3 = h</span></p> <p><span XXXXX="s1"><span XXXXX="XXXXX-converted-space"> </span>y = 3h<span XXXXX="Apple-XXXXXXXXX-space"></span></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 XXXXX="s1"></span> </p> <p><span XXXXX="s1">XXXXX</span></p> <p><span XXXXX="s1">Document 4: Modern XXX Totalitarianism/XXXXXXXXXXXX: A Study of XXXXX XXXXX<span class="XXXXX-converted-space"></span></span></p> <p><span XXXXX="XX">XXXX XXXXXXXXXX context XXX you XXXXXXX XX the XXXXX Korean Government XXXX is associated with XXX enduring XXXXX you XXXXX?</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX" <the="" enduring="" XXXXX="" XXXX="" XXXX="" interests="" me="" is="" the="" XX="" human="" XXXXXX.="" according="" to="" un,="" rights="" XXX="" belong="" XXX="" XXXXXX,="" regardless="" their="" XXXXXX,="" XXXXXX="" XXXXXX,="" XXXXXX="" identity,="" XXXXXXXXXX="" background,="" faith="" or="" other="" XXXXXXXXXXX="" XXXXXXXXXXX.="" these="" XXXXXXX="" right="" XXXX="" XXX="" XXXXXXX,="" freedom="" from="" XXXXXXX="" XXXXXXXXXXX,="" XXXXXXX="" XXXXX,="" XXXXX="" work="" for="" a="" XXXX="" wage,="" so="" on.="" XXXXX="" korea’s="" historical="" XXXXXXX="" grim,="" its="" record="" XXXXXX.="" XXXXXXX,="" XXXX="" XX="" XXXXXXXXXX="" XXXXXXX="" XXXXX="" XXXXXXXXXX="" committed="" XXXXX,="" XXXXXXXXXX="" XXXXXXXXXX="" XXXXXX,="" XXXXXXXXX="" extermination,="" XXXXXXX,="" XXXX="" XXXXXXXXXXXX.="">span class="Apple-XXXXXXXXX-space"></span></p> <p><span class="s1"></span> </p> <p><span XXXXX="s1">XXXXX XXXXX was XXXXXX out XX XXX XXXXXXXXXX XXXXXXXXXX XX Kim XX-XXXX, a post-XXX XXXXXXXXXXX XXXXXXXXX who XXXXXXXXX XXX civil liberties XX XXX North Korean XXXXXX in order XX XXXX with XXXXXXXX emergencies such as the XXXXXX XXX. Furthermore, Kim Il-Sung and XXX XXXXXXXXXXX XXXX continued XX consolidate XXXXX in a way that XXXXXXXX XXXXX rights in XXXXX XXXXX. XXXX have created a regime XXXXX XXXX XXXXXX is XXXXXXXXXX, XXX where XXXXXXXX XXXXXXXXX XXXXXXXXX XXXXX XXXXX rights. XXXXX XXXXXXX XXX XXX of XXXXXXX, XXXXXX labor XXX XXXXXXXXXXXXX in XXXXXXXX XXXXXXXXXX. XXXXX is also no XXXXXXXXXXX XXX process within the XXXXXXXX XXXXXX. The XXXX of XXXXX XXXXXX in XXXXX Korea is a result XX decades of XXXXXXXXXXXXX by the XXXXX Korean communist XXXXXXXXXXXX, in a XXX XX continue their XXXX grip XX power over the XXXXXXX.<span XXXXX="XXXXX-converted-XXXXX"></span></span></p> <p><span class="XX"></span> </p> <p><span XXXXX="s1">XXX XXXX the XXXXX of power/human XXXXXX in the XXXXXXXXXX XX North XXXXX XXXXXX people?</span></p> <p><span class="XX"></span> </p> <p><span class="s1" <the="" north="" XXXXXX="" XXXXXX="" XXX="" affected="" in="" three="" XXXX="" XXXX:="" XXXXXX,="" inhumane="" imprisonment="" and="" forced="" labor.="" XXXXXXXX,="" chronic="" XXXXXXXXXXXXX="" XX="" the="" economy="" has="" led="" XX="" XXXXXXXXXX="" multiple="" famines="" over="" their="" XXXXXXXX.="" this="" deprived="" XXXX="" XXXXXXX="" work="" XXXX.="" XXXXXXXXXXX,="" koreans="" unable="" access="" free="" XXXXX="" XXXX="" XX="" XXX="" york="" XXXXX,="" XXXXX="" XXXXXX="" XXXXX="" XXXXXX.="" also="" XXX="" XXXX,="" XXXX="" movement="" XXXXXXX="" highly="" XXXXXXXXXXX="" XXXXX="" through="" border="" XXXXXXXX="" military="" checkpoints.="" XXXXXXX,="" political="" XXXXXXXXX="" XXXXXXXXX="" have="" human="" rights="" XXXXXXXX="" labor,="" torture,="" XXXXX="" conditions.="" noted="" passage,="" XXXXX="" XXXXXXXX="" XXXXXXXXX="" prison="" camps="" XXXXX="" XXXXXXXXX="" opponents="" XXXXXXXXXX="" sent="" face="" XXXXXXXXXX="" XXXXXXX="">span XXXXX="XXXXX-XXXXXXXXX-XXXXX"&XX;</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="XX"></span> </p> <p><span class="XX">84417</span></p> <p><span class="XX">Unit 2 Exam</span></p> <p><span XXXXX="s1"></span> </p> <p><span class="s1"><span class="Apple-converted-XXXXX"></span>X. X.<span class="Apple-XXXXXXXXX-XXXXX"></span></span></p> <p><span class="XX">X. X.</span></p> <p><span XXXXX="s1">9. X.</span></p> <p><span XXXXX="XX">XX. 4.</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="XX"></span> </p> <p><span class="XX"></span> </p> <p><span class="XX"></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="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 XXXXX="XX"></span> </p> <p><span XXXXX="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="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="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">76432</span></p> <p><span XXXXX="XX">Literal XXXXXXXXX: Worksheet #1</span></p> <p><span class="s1">6a.<span XXXXX="Apple-converted-XXXXX"></span></span></p> <p><span class="s1">XX = XX + XX</span></p> <p><span class="s1">2x = 26 - XX</span></p> <p><span XXXXX="s1">x = 12 / 2</span></p> <p><span XXXXX="XX">x = 6</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">6b. XX = 7v + 5</span></p> <p><span XXXXX="s1">7v = XX - X</span></p> <p><span XXXXX="XX">v = (3d - X) /7</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">XX. -30 = X - 8x</span></p> <p><span class="XX"><span class="XXXXX-converted-XXXXX"> </span>8x = X + XX</span></p> <p><span class="s1"><span XXXXX="Apple-converted-XXXXX"> </span>x = XX/X</span></p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">XX. 7a = XX - 2h</span></p> <p><span XXXXX="XX"><span class="XXXXX-XXXXXXXXX-space"> </span>2h = 10 - XX</span></p> <p><span class="s1"><span class="XXXXX-XXXXXXXXX-space"> </span>h = (10 - XX) /2</span></p> <p><span class="s1"></span> </p> <p><span class="XX">XX. X(x-X) = 12</span></p> <p><span class="XX"><span class="XXXXX-converted-XXXXX"> </span>3x - 12 = 12</span></p> <p><span XXXXX="XX"><span class="XXXXX-XXXXXXXXX-XXXXX"> </span>XX = 24</span></p> <p><span class="XX"><span class="XXXXX-XXXXXXXXX-XXXXX"> </span>x = X</span></p> <p><span class="s1"></span> </p> <p><span XXXXX="XX">8b. X(XX + p) = w</span></p> <p><span XXXXX="s1"><span class="XXXXX-converted-space"> </span>XXX + XX = w</span></p> <p><span class="s1"><span XXXXX="XXXXX-converted-space"> </span>5p = w - 20x</span></p> <p><span class="XX"><span XXXXX="Apple-converted-XXXXX"> </span>p = (w - XXX) / 5<span class="Apple-XXXXXXXXX-XXXXX"></span></span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX">Which XX equivalent XX XX - 8b = 10x</span></p> <p><span XXXXX="s1">a = (10x + 8b) / 7</span></p> <p><span XXXXX="s1">The XXXXXX is B</span></p> <p><span class="XX"></span> </p> <p><span XXXXX="XX"></span> </p> <p><span XXXXX="s1">Which is XXXXXXXXXX to 4ab + X = XX</span></p> <p><span XXXXX="XX">X = XX - 4ab</span></p> <p><span class="s1">XXX XXXXXX XX C</span></p> <p><span class="XX"></span> </p><p><br></p>">
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