Year 11 Solving Linear Inequalities Worksheet — Level 3 — Practice Set 2 — 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 2 — Answers
Solve each inequality. When you multiply or divide both sides by a negative number, reverse the inequality sign.
1.Solve: x − 2 > −10
Answer: x > −8
- Add 2: x > −8
- Divide by 1: x > −8
2.Solve: −4x + 3 ≤ −45
Answer: x ≥ 12
- Subtract 3: −4x ≤ −48
- Divide by −4 (negative, so reverse the sign): x ≥ 12
3.Solve: −2x − 11 ≤ −35
Answer: x ≥ 12
- Add 11: −2x ≤ −24
- Divide by −2 (negative, so reverse the sign): x ≥ 12
4.Solve: 4x + 6 > 2
Answer: x > −1
- Subtract 6: 4x > −4
- Divide by 4: x > −1
5.Solve: −5x + 3 < 43
Answer: x > −8
- Subtract 3: −5x < 40
- Divide by −5 (negative, so reverse the sign): x > −8
6.Solve: −5x + 8 < −22
Answer: x > 6
- Subtract 8: −5x < −30
- Divide by −5 (negative, so reverse the sign): x > 6
7.Solve: −x − 12 ≥ −9
Answer: x ≤ −3
- Add 12: −x ≥ 3
- Divide by −1 (negative, so reverse the sign): x ≤ −3
8.Solve: 2x + 12 ≥ 12
Answer: x ≥ 0
- Subtract 12: 2x ≥ 0
- Divide by 2: x ≥ 0
9.Solve: x + 12 < 20
Answer: x < 8
- Subtract 12: x < 8
- Divide by 1: x < 8
10.Solve: −3x + 9 ≥ −9
Answer: x ≤ 6
- Subtract 9: −3x ≥ −18
- Divide by −3 (negative, so reverse the sign): x ≤ 6
11.Solve: −5x + 3 ≥ 28
Answer: x ≤ −5
- Subtract 3: −5x ≥ 25
- Divide by −5 (negative, so reverse the sign): x ≤ −5
12.Solve: 6x + 1 < 73
Answer: x < 12
- Subtract 1: 6x < 72
- Divide by 6: x < 12
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.