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.
1.3x < 3
Answer: x < 1
- Divide both sides by 3 (positive, so the sign stays): x < 1
2.x + 9 > 18
Answer: x > 9
- Subtract 9 on both sides: x > 18 − 9 = 9
3.2x > 20
Answer: x > 10
- Divide both sides by 2 (positive, so the sign stays): x > 10
4.x + 2 ≥ 1
Answer: x ≥ −1
- Subtract 2 on both sides: x ≥ 1 − 2 = −1
5.x − 5 ≤ −10
Answer: x ≤ −5
- Add 5 on both sides: x ≤ −10 + 5 = −5
6.x + 1 ≤ −3
Answer: x ≤ −4
- Subtract 1 on both sides: x ≤ −3 − 1 = −4
7.6x ≥ −30
Answer: x ≥ −5
- Divide both sides by 6 (positive, so the sign stays): x ≥ −5
8.x − 3 ≥ 9
Answer: x ≥ 12
- Add 3 on both sides: x ≥ 9 + 3 = 12
9.x + 1 ≤ −4
Answer: x ≤ −5
- Subtract 1 on both sides: x ≤ −4 − 1 = −5
10.x + 5 ≥ 0
Answer: x ≥ −5
- Subtract 5 on both sides: x ≥ 0 − 5 = −5
11.x + 4 > −4
Answer: x > −8
- Subtract 4 on both sides: x > −4 − 4 = −8
12.x − 1 < −6
Answer: x < −5
- Add 1 on both sides: x < −6 + 1 = −5
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.