Year 10 Solving Linear Inequalities Worksheet — Level 1 — Practice Set 3 — 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 1 — Practice Set 3 — Answers
Solve each inequality the same way you would solve an equation.
1.x − 8 ≥ −6
Answer: x ≥ 2
- Add 8 on both sides: x ≥ −6 + 8 = 2
2.x + 8 ≤ 9
Answer: x ≤ 1
- Subtract 8 on both sides: x ≤ 9 − 8 = 1
3.6x ≥ 60
Answer: x ≥ 10
- Divide both sides by 6 (positive, so the sign stays): x ≥ 10
4.x − 5 > −7
Answer: x > −2
- Add 5 on both sides: x > −7 + 5 = −2
5.x + 5 < 1
Answer: x < −4
- Subtract 5 on both sides: x < 1 − 5 = −4
6.8x ≥ 56
Answer: x ≥ 7
- Divide both sides by 8 (positive, so the sign stays): x ≥ 7
7.2x > 18
Answer: x > 9
- Divide both sides by 2 (positive, so the sign stays): x > 9
8.x − 9 < −7
Answer: x < 2
- Add 9 on both sides: x < −7 + 9 = 2
9.9x < −9
Answer: x < −1
- Divide both sides by 9 (positive, so the sign stays): x < −1
10.2x ≤ −16
Answer: x ≤ −8
- Divide both sides by 2 (positive, so the sign stays): x ≤ −8
11.x + 2 > 3
Answer: x > 1
- Subtract 2 on both sides: x > 3 − 2 = 1
12.x − 6 < −12
Answer: x < −6
- Add 6 on both sides: x < −12 + 6 = −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.
- Celebrate what went well first, then pick one thing to work on next.