Question

1. -2(x + 1)+8=-14
2. 10 - 31(6t - 9)=1
3. 2(4n + 1)-3n=17
4. 7 - 3(2c - 5)+c=58
5. -5x + 4(x - 6)=1
6. 9(y + 2)-4y + 1=49
7. 4 - 6(v + 3)+2v=-2

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:

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