Math worksheet titled "Solving Inequalities Worksheet" featuring eight inequality problems with corresponding number lines for graphing solutions.

I'll solve each inequality step by step, then provide the final answers.

Problem 1: 2q - 4q ≤ -2
- Combine like terms: -2q ≤ -2
- Divide both sides by -2 (flip the inequality sign): q ≥ 1

Problem 2: n - 8 < -8
- Add 8 to both sides: n < 0

Problem 3: k - 8 > 15
- Add 8 to both sides: k > 23

Problem 4: 0 ≤ 2p + 3p
- Combine like terms: 0 ≤ 5p
- Divide both sides by 5: 0 ≤ p or p ≥ 0

Problem 5: -5(1 - 4s) > -5
- Distribute: -5 + 20s > -5
- Add 5 to both sides: 20s > 0
- Divide by 20: s > 0

Problem 6: 5 + y ≤ -13
- Subtract 5 from both sides: y ≤ -18

Problem 7: -6 > 5n + 5 + 4
- Simplify right side: -6 > 5n + 9
- Subtract 9 from both sides: -15 > 5n
- Divide by 5: -3 > n or n < -3

Problem 8: 9 < b - 2
- Add 2 to both sides: 11 < b or b > 11

Final Answer:
1. q ≥ 1
2. n < 0
3. k > 23
4. p ≥ 0
5. s > 0
6. y ≤ -18
7. n < -3
8. b > 11