Question

1. |3m - 3| = 12
2. |-2x + 8| = 20
3. |d| + 3 = 5
4. |t| - 9 = 15
5. 4|x| = 32
6. |b|/7 = 3
7. -3|f + 4| = -27
8. |4x - 8| + 3 = 11

Explanation:

Step1: Solve equation 7 |3m - 3| = 12

Set up two - cases:
Case 1: 3m - 3=12. Add 3 to both sides: 3m=12 + 3=15. Divide both sides by 3, m = 5.
Case 2: 3m - 3=-12. Add 3 to both sides: 3m=-12 + 3=-9. Divide both sides by 3, m=-3.

Step2: Solve equation 8 |-2x + 8| = 20

Set up two - cases:
Case 1: -2x + 8=20. Subtract 8 from both sides: -2x=20 - 8 = 12. Divide both sides by -2, x=-6.
Case 2: -2x + 8=-20. Subtract 8 from both sides: -2x=-20 - 8=-28. Divide both sides by -2, x = 14.

Step3: Solve equation 9 |d|+3 = 5

Subtract 3 from both sides: |d|=5 - 3 = 2. So d = 2 or d=-2.

Step4: Solve equation 10 |t|-9 = 15

Add 9 to both sides: |t|=15 + 9 = 24. So t = 24 or t=-24.

Step5: Solve equation 11 4|x| = 32

Divide both sides by 4: |x| = 8. So x = 8 or x=-8.

Step6: Solve equation 12 |b|/7=3

Multiply both sides by 7: |b|=21. So b = 21 or b=-21.

Step7: Solve equation 13 - 3|f + 4|=-27

Divide both sides by -3: |f + 4| = 9.
Set up two - cases:
Case 1: f + 4=9. Subtract 4 from both sides, f = 5.
Case 2: f + 4=-9. Subtract 4 from both sides, f=-13.

Step8: Solve equation 14 |4x - 8|+3 = 11

Subtract 3 from both sides: |4x - 8|=11 - 3 = 8.
Set up two - cases:
Case 1: 4x - 8=8. Add 8 to both sides: 4x=8 + 8 = 16. Divide both sides by 4, x = 4.
Case 2: 4x - 8=-8. Add 8 to both sides: 4x=-8 + 8 = 0. Divide both sides by 4, x = 0.

Answer:

1. m = 5 or m=-3
2. x=-6 or x = 14
3. d = 2 or d=-2
4. t = 24 or t=-24
5. x = 8 or x=-8
6. b = 21 or b=-21
7. f = 5 or f=-13
8. x = 4 or x = 0