Year 9 Solving Linear Inequalities Worksheet — Level 3 — Practice Set 3 — 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 3 — Answers
Solve each inequality. When you multiply or divide both sides by a negative number, reverse the inequality sign.
1.Solve: 6x − 11 > 49
Answer: x > 10
- Add 11: 6x > 60
- Divide by 6: x > 10
2.Solve: 5x + 12 ≥ 12
Answer: x ≥ 0
- Subtract 12: 5x ≥ 0
- Divide by 5: x ≥ 0
3.Solve: 3x + 6 ≥ 3
Answer: x ≥ −1
- Subtract 6: 3x ≥ −3
- Divide by 3: x ≥ −1
4.Solve: x + 2 > 3
Answer: x > 1
- Subtract 2: x > 1
- Divide by 1: x > 1
5.Solve: −4x − 5 < −1
Answer: x > −1
- Add 5: −4x < 4
- Divide by −4 (negative, so reverse the sign): x > −1
6.Solve: −6x + 2 ≤ 44
Answer: x ≥ −7
- Subtract 2: −6x ≤ 42
- Divide by −6 (negative, so reverse the sign): x ≥ −7
7.Solve: −2x − 9 < −29
Answer: x > 10
- Add 9: −2x < −20
- Divide by −2 (negative, so reverse the sign): x > 10
8.Solve: −2x + 6 < 24
Answer: x > −9
- Subtract 6: −2x < 18
- Divide by −2 (negative, so reverse the sign): x > −9
9.Solve: −3x + 1 ≥ −2
Answer: x ≤ 1
- Subtract 1: −3x ≥ −3
- Divide by −3 (negative, so reverse the sign): x ≤ 1
10.Solve: −3x + 1 < −17
Answer: x > 6
- Subtract 1: −3x < −18
- Divide by −3 (negative, so reverse the sign): x > 6
11.Solve: 3x − 7 > −19
Answer: x > −4
- Add 7: 3x > −12
- Divide by 3: x > −4
12.Solve: 2x − 4 > 0
Answer: x > 2
- Add 4: 2x > 4
- Divide by 2: x > 2
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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