9. -2(x + 1)+8=-14\n10. 10 - 31(6t - 9)=1\n11. 2(4n + 1)-3n=17\n12. 7 - 3(2c - 5)+c=58\n13. -5x + 4(x…

Explanation:

Step1: Solve -2(x + 1)+8=-14

First, distribute -2: -2x-2 + 8=-14 Combine like - terms: -2x+6=-14 Subtract 6 from both sides: -2x=-14 - 6=-20 Divide both sides by -2: $x = 10$

Step2: Solve 10-31(6t - 9)=1

Distribute -31: 10-186t + 279=1 Combine like - terms: 289-186t=1 Subtract 289 from both sides: -186t=1 - 289=-288 Divide both sides by -186: $t=\frac{-288}{-186}=\frac{48}{31}$

Step3: Solve 2(4n + 1)-3n=17

Distribute 2: 8n+2-3n=17 Combine like - terms: 5n+2=17 Subtract 2 from both sides: 5n=17 - 2 = 15 Divide both sides by 5: $n = 3$

Step4: Solve 7-3(2c - 5)+c=58

Distribute -3: 7-6c + 15+c=58 Combine like - terms: 22-5c=58 Subtract 22 from both sides: -5c=58 - 22 = 36 Divide both sides by -5: $c=-\frac{36}{5}$

Step5: Solve -5x+4(x - 6)=1

Distribute 4: -5x+4x-24=1 Combine like - terms: -x-24=1 Add 24 to both sides: -x=1 + 24 = 25 Multiply both sides by -1: $x=-25$

Step6: Solve 9(y + 2)-4y+1=49

Distribute 9: 9y+18-4y + 1=49 Combine like - terms: 5y+19=49 Subtract 19 from both sides: 5y=49 - 19 = 30 Divide both sides by 5: $y = 6$

Step7: Solve 4-6(v + 3)+2v=-2

Distribute -6: 4-6v-18 + 2v=-2 Combine like - terms: -4v-14=-2 Add 14 to both sides: -4v=-2 + 14 = 12 Divide both sides by -4: $v=-3$

Answer:

$x = 10,t=\frac{48}{31},n = 3,c=-\frac{36}{5},x=-25,y = 6,v=-3$