Year 11 Solving Linear Inequalities Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 11 linear equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Linear EquationsYear 11 Solving Linear Inequalities Worksheet — Level 3 — Practice Set 4 — Answers
Solve each inequality. When you multiply or divide both sides by a negative number, reverse the inequality sign.
1.Solve: 6x + 1 ≤ −5
Answer: x ≤ −1
- Subtract 1: 6x ≤ −6
- Divide by 6: x ≤ −1
2.Solve: −4x + 3 ≥ −9
Answer: x ≤ 3
- Subtract 3: −4x ≥ −12
- Divide by −4 (negative, so reverse the sign): x ≤ 3
3.Solve: 6x + 2 ≥ 38
Answer: x ≥ 6
- Subtract 2: 6x ≥ 36
- Divide by 6: x ≥ 6
4.Solve: −5x − 1 < 29
Answer: x > −6
- Add 1: −5x < 30
- Divide by −5 (negative, so reverse the sign): x > −6
5.Solve: 4x − 1 > 43
Answer: x > 11
- Add 1: 4x > 44
- Divide by 4: x > 11
6.Solve: −3x + 6 ≤ −6
Answer: x ≥ 4
- Subtract 6: −3x ≤ −12
- Divide by −3 (negative, so reverse the sign): x ≥ 4
7.Solve: −6x − 10 > −52
Answer: x < 7
- Add 10: −6x > −42
- Divide by −6 (negative, so reverse the sign): x < 7
8.Solve: −5x − 11 > −46
Answer: x < 7
- Add 11: −5x > −35
- Divide by −5 (negative, so reverse the sign): x < 7
9.Solve: −5x + 10 < 30
Answer: x > −4
- Subtract 10: −5x < 20
- Divide by −5 (negative, so reverse the sign): x > −4
10.Solve: −2x + 3 ≤ 7
Answer: x ≥ −2
- Subtract 3: −2x ≤ 4
- Divide by −2 (negative, so reverse the sign): x ≥ −2
11.Solve: −x − 9 > −2
Answer: x < −7
- Add 9: −x > 7
- Divide by −1 (negative, so reverse the sign): x < −7
12.Solve: 5x − 9 > −39
Answer: x > −6
- Add 9: 5x > −30
- Divide by 5: x > −6
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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