Year 10 Solving Linear Inequalities Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 10 linear equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Linear EquationsYear 10 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: −3x + 3 ≤ 18
Answer: x ≥ −5
- Subtract 3: −3x ≤ 15
- Divide by −3 (negative, so reverse the sign): x ≥ −5
2.Solve: −x + 2 > 9
Answer: x < −7
- Subtract 2: −x > 7
- Divide by −1 (negative, so reverse the sign): x < −7
3.Solve: −3x − 2 > 22
Answer: x < −8
- Add 2: −3x > 24
- Divide by −3 (negative, so reverse the sign): x < −8
4.Solve: −4x − 11 ≥ −59
Answer: x ≤ 12
- Add 11: −4x ≥ −48
- Divide by −4 (negative, so reverse the sign): x ≤ 12
5.Solve: 5x + 4 ≤ 19
Answer: x ≤ 3
- Subtract 4: 5x ≤ 15
- Divide by 5: x ≤ 3
6.Solve: 3x + 11 < 29
Answer: x < 6
- Subtract 11: 3x < 18
- Divide by 3: x < 6
7.Solve: −2x − 4 ≥ 0
Answer: x ≤ −2
- Add 4: −2x ≥ 4
- Divide by −2 (negative, so reverse the sign): x ≤ −2
8.Solve: −x + 6 > 7
Answer: x < −1
- Subtract 6: −x > 1
- Divide by −1 (negative, so reverse the sign): x < −1
9.Solve: −4x − 1 ≤ −1
Answer: x ≥ 0
- Add 1: −4x ≤ 0
- Divide by −4 (negative, so reverse the sign): x ≥ 0
10.Solve: 2x − 4 > 18
Answer: x > 11
- Add 4: 2x > 22
- Divide by 2: x > 11
11.Solve: 5x − 3 > 52
Answer: x > 11
- Add 3: 5x > 55
- Divide by 5: x > 11
12.Solve: 5x − 10 ≥ −30
Answer: x ≥ −4
- Add 10: 5x ≥ −20
- Divide by 5: x ≥ −4
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.