Year 9 Solving Linear Inequalities Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 9 linear equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Linear EquationsYear 9 Solving Linear Inequalities Worksheet — Level 3 — Practice Set 2 — Answers
Solve each inequality. When you multiply or divide both sides by a negative number, reverse the inequality sign.
1.Solve: 4x − 12 < 32
Answer: x < 11
- Add 12: 4x < 44
- Divide by 4: x < 11
2.Solve: −x − 7 ≥ −18
Answer: x ≤ 11
- Add 7: −x ≥ −11
- Divide by −1 (negative, so reverse the sign): x ≤ 11
3.Solve: −4x − 1 < −9
Answer: x > 2
- Add 1: −4x < −8
- Divide by −4 (negative, so reverse the sign): x > 2
4.Solve: 5x + 9 ≥ −31
Answer: x ≥ −8
- Subtract 9: 5x ≥ −40
- Divide by 5: x ≥ −8
5.Solve: 3x − 5 ≤ −14
Answer: x ≤ −3
- Add 5: 3x ≤ −9
- Divide by 3: x ≤ −3
6.Solve: x − 4 > 5
Answer: x > 9
- Add 4: x > 9
- Divide by 1: x > 9
7.Solve: 5x − 7 < −7
Answer: x < 0
- Add 7: 5x < 0
- Divide by 5: x < 0
8.Solve: −5x − 3 ≥ −33
Answer: x ≤ 6
- Add 3: −5x ≥ −30
- Divide by −5 (negative, so reverse the sign): x ≤ 6
9.Solve: −2x − 4 > 6
Answer: x < −5
- Add 4: −2x > 10
- Divide by −2 (negative, so reverse the sign): x < −5
10.Solve: 2x − 5 ≥ −11
Answer: x ≥ −3
- Add 5: 2x ≥ −6
- Divide by 2: x ≥ −3
11.Solve: −3x + 9 ≤ −18
Answer: x ≥ 9
- Subtract 9: −3x ≤ −27
- Divide by −3 (negative, so reverse the sign): x ≥ 9
12.Solve: x + 3 < 14
Answer: x < 11
- Subtract 3: x < 11
- Divide by 1: x < 11
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.