Question

1. -8 + 2x ≥ 4
2. 4 > 3v + 22
3. 4(6u + 9) ≤ 19u + 11
4. 2(4 - w) + 2w > 13
5. -20 < 19 + y
6. 12 > -4x
7. 5 ≥ \frac{w}{7}
8. x - 3 > 25

Explanation:

Step1: Solve -8 + 2x ≥ 4

Add 8 to both sides: 2x ≥ 4 + 8, 2x ≥ 12. Then divide both sides by 2, x ≥ 6.

Step2: Solve 4 > 3v+22

Subtract 22 from both sides: 4 - 22 > 3v, -18 > 3v. Divide both sides by 3, - 6 > v or v < -6.

Step3: Solve 4(6u + 9) ≤ 19u+11

Expand the left - hand side: 24u+36 ≤ 19u + 11. Subtract 19u from both sides: 24u-19u+36 ≤ 11, 5u+36 ≤ 11. Subtract 36 from both sides: 5u ≤ 11 - 36, 5u ≤ -25. Divide both sides by 5, u ≤ -5.

Step4: Solve 2(4 - w)+2w > 13

Expand the left - hand side: 8-2w + 2w>13, 8>13, which is a contradiction, so the solution set is the empty set ∅.

Step5: Solve -20 < 19 + y

Subtract 19 from both sides: -20 - 19 < y, -39 < y or y > -39.

Step6: Solve 12 > -4x

Divide both sides by -4 and reverse the inequality sign: 12/(-4)<x, -3 < x or x > -3.

Step7: Solve 5 ≥ w/7

Multiply both sides by 7: 5×7 ≥ w, 35 ≥ w or w ≤ 35.

Step8: Solve x - 3 > 25

Add 3 to both sides: x > 25 + 3, x > 28.

Answer:

1. x ≥ 6
2. v < -6
3. u ≤ -5
4. ∅
5. y > -39
6. x > -3
7. w ≤ 35
8. x > 28