Year 7 Solving Linear Inequalities Worksheet — Level 1 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 7 linear equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 7 · Mathematics · Linear EquationsYear 7 Solving Linear Inequalities Worksheet — Level 1 — Practice Set 3 — Answers
Solve each inequality the same way you would solve an equation.
1.2x < 18
Answer: x < 9
- Divide both sides by 2 (positive, so the sign stays): x < 9
2.x + 5 ≤ −2
Answer: x ≤ −7
- Subtract 5 on both sides: x ≤ −2 − 5 = −7
3.x + 2 < 1
Answer: x < −1
- Subtract 2 on both sides: x < 1 − 2 = −1
4.x − 8 > −15
Answer: x > −7
- Add 8 on both sides: x > −15 + 8 = −7
5.3x ≥ 30
Answer: x ≥ 10
- Divide both sides by 3 (positive, so the sign stays): x ≥ 10
6.3x > 18
Answer: x > 6
- Divide both sides by 3 (positive, so the sign stays): x > 6
7.x − 9 ≥ −12
Answer: x ≥ −3
- Add 9 on both sides: x ≥ −12 + 9 = −3
8.6x < −12
Answer: x < −2
- Divide both sides by 6 (positive, so the sign stays): x < −2
9.x + 8 ≤ 15
Answer: x ≤ 7
- Subtract 8 on both sides: x ≤ 15 − 8 = 7
10.x − 4 ≤ −11
Answer: x ≤ −7
- Add 4 on both sides: x ≤ −11 + 4 = −7
11.x + 5 ≤ −3
Answer: x ≤ −8
- Subtract 5 on both sides: x ≤ −3 − 5 = −8
12.8x ≥ 48
Answer: x ≥ 6
- Divide both sides by 8 (positive, so the sign stays): 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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