hey student, note: please read and understand the answer file the answer file consists of complete answers and explanations to 12 algebra problems the answers and explanations are complete the answers and explanations have been properly solved, correct and checked. simplify each expression. 1. 10x - 8x + 2 + 10 10x - 8x + 2 + 10 can be simplified by combining the like terms: = 2x + 12 therefore, the simplified expression is 2x + 12. 2. 3a + 7 + 2(3 + a) 3a + 7 + 2(3 + a) can be simplified using the distributive property and combining like terms: = 3a + 7 + 6 + 2a (distributing the 2 to 3 and a inside the parentheses) = 5a + 13 (combining like terms) therefore, the simplified expression is 5a + 13. 3. 3(m - 5) + m 3(m - 5) + m can be simplified using the distributive property and combining like terms: = 3m - 15 + m (distributing the 3 to m and -5 inside the parentheses) = 4m - 15 (combining like terms) therefore, the simplified expression is 4m - 15. 4. 2s + 10 - 7s - 8 + 3s - 7 2s + 10 - 7s - 8 + 3s - 7 can be simplified by combining the like terms: = -2s - 5 therefore, the simplified expression is -2s - 5. 5. 8c - 4 - 2c + 5 8c - 4 - 2c + 5 can be simplified by combining the like terms: = 6c + 1 therefore, the simplified expression is 6c + 1. 6. -4 + 7z + 3 - 2z -4 + 7z + 3 - 2z can be simplified by combining the like terms: = 5z - 1 therefore, the simplified expression is 5z - 1. 7. 15 + 4(5y - 10) 15 + 4(5y - 10) can be simplified using the distributive property: = 15 + 20y - 40 (distributing the 4 to 5y and -10 inside the parentheses) = 20y - 25 (combining like terms) therefore, the simplified expression is 20y - 25. 8. 2d + 17 - 3 - 2d + 4d 2d + 17 - 3 - 2d + 4d can be simplified by combining the like terms: = 4d + 14 therefore, the simplified expression is 4d + 14. 9. 12n - 8 - 2n + 10 - 4 12n - 8 - 2n + 10 - 4 can be simplified by combining the like terms: = 10n - 2 therefore, the simplified expression is 10n - 2. 10. 8(2k + 1 + 3k) 8(2k + 1 + 3k) can be simplified using the distributive property: = 16k + 8 + 24k (distributing the 8 to 2k, 1, and 3k inside the parentheses) = 40k + 8 (combining like terms) therefore, the simplified expression is 40k + 8. 11. 4(2b + 2) - 3 4(2b + 2) - 3 can be simplified using the distributive property: = 8b + 8 - 3 (distributing the 4 to 2b and 2 inside the parentheses) = 8b + 5 (combining like terms) therefore, the simplified expression is 8b + 5. 12. -4 + 8p - 6p - 5 + 20p -4 + 8p - 6p - 5 + 20p can be simplified by combining the like terms: = 22p - 9 therefore, the simplified expression is 22p - 9.

1. 2x + 122. 3a + 7 + 6 + 2a = 5a + 133. 3m - 15 + m = 4m - 154. 2s - 7s + 3s + 10 -8 -7 = -2s -55. 8c - 2c - 4 + 5 = 6c +16. -4 + 3 + 7z -2z = -1 + 5z7. 15 + 20y -40 = 20y - 258. 2d -2d + 4d + 17 - 3 = 4d +149. 12n - 2n - 8 + 10 - 4 = 10n - 210. 16k + 8 + 24k = 40k + 811. 8b + 8 - 3 = 8b + 512. 8p - 6p + 20p - 4 - 5 = 22p - 9

1) 10x - 8x + 2 + 10 = 2x + 12 2) 3a + 7 + 2(3 + a) = 3a + 7 + 6 + 2a = 3a - 2a + 7 + 6 = a + 13 3) 3(m-5) + m = 3m - 15 + m = 3m + m - 15 = 4m + 15 4) 2s + 10 - 7s - 8 + 3s - 7 = 2s - 7s + 3s + 10 - 8 - 7 = -7s - 5 5) 8c - 4 - 2c + 5 = 8c - 2c - 4 + 5 = 6c + 1 6) -4 + 7z + 3 - 2z = 7z - 2z - 4 + 3 = 5z - 1 7) 15 + 4(5y - 10) = 15 + 20y - 40 = 20y + 15 - 40 = 20y - 25 8) 2d + 17 - 3 - 2d + 4d = 2d - 2d + 4d + 17 - 3 = 4d + 14 9) 12n - 8 - 2n + 10 - 4 = 12n - 2n - 8 + 10 - 4 = 10n - 2 10) 8( 2k + 1 + 3k ) = 8( 2k + 3k + 1 ) = 8(5k + 1) = 40k + 8 11) 4(2b + 2) - 3 = 8b + 8 -3 = 8b + 5 12) -4 + 8p - 6p - 5 + 20p = 8p - 6p + 20p - 4 - 5 = 22p - 9

solutions for each expression: 1). 10x-8x+2+10 = 2x+12 2). 3a+7+2(3+a) = 5a+13 3). 3(m-5)+m = 4m-15 4). 2s+10-7s-8+3s-7 = -2s-5 5). 8c-4-2c+5 = 6c+1 6). -4+7z+3-2z = 5z-1 7). 15+ 4(5y-10) = 20y-5 8). 2d+17-3-2d+4d = 4d+14 9). 12n-8-2n+10-4 = 10n-2 10). 8(2k+1+3k) = 40k+8