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: −2x + 5 > 11
Answer: x < −3
- Subtract 5: −2x > 6
- Divide by −2 (negative, so reverse the sign): x < −3
2.Solve: 4x − 11 < 1
Answer: x < 3
- Add 11: 4x < 12
- Divide by 4: x < 3
3.Solve: −x − 12 ≥ −17
Answer: x ≤ 5
- Add 12: −x ≥ −5
- Divide by −1 (negative, so reverse the sign): x ≤ 5
4.Solve: −5x + 10 < 5
Answer: x > 1
- Subtract 10: −5x < −5
- Divide by −5 (negative, so reverse the sign): x > 1
5.Solve: −6x − 10 ≥ 26
Answer: x ≤ −6
- Add 10: −6x ≥ 36
- Divide by −6 (negative, so reverse the sign): x ≤ −6
6.Solve: 5x + 12 > 22
Answer: x > 2
- Subtract 12: 5x > 10
- Divide by 5: x > 2
7.Solve: 2x − 10 ≤ 0
Answer: x ≤ 5
- Add 10: 2x ≤ 10
- Divide by 2: x ≤ 5
8.Solve: −2x + 12 > 2
Answer: x < 5
- Subtract 12: −2x > −10
- Divide by −2 (negative, so reverse the sign): x < 5
9.Solve: −3x + 9 ≤ 9
Answer: x ≥ 0
- Subtract 9: −3x ≤ 0
- Divide by −3 (negative, so reverse the sign): x ≥ 0
10.Solve: −x − 9 ≥ −5
Answer: x ≤ −4
- Add 9: −x ≥ 4
- Divide by −1 (negative, so reverse the sign): x ≤ −4
11.Solve: 4x − 2 ≤ −38
Answer: x ≤ −9
- Add 2: 4x ≤ −36
- Divide by 4: x ≤ −9
12.Solve: 4x − 6 ≥ −38
Answer: x ≥ −8
- Add 6: 4x ≥ −32
- Divide by 4: x ≥ −8
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.
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