Year 8 Solving Linear Inequalities Worksheet — Level 1 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 8 linear equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Linear EquationsYear 8 Solving Linear Inequalities Worksheet — Level 1 — Practice Set 3 — Answers
Solve each inequality the same way you would solve an equation.
1.3x ≤ 21
Answer: x ≤ 7
- Divide both sides by 3 (positive, so the sign stays): x ≤ 7
2.8x < 32
Answer: x < 4
- Divide both sides by 8 (positive, so the sign stays): x < 4
3.x + 5 ≥ −4
Answer: x ≥ −9
- Subtract 5 on both sides: x ≥ −4 − 5 = −9
4.6x ≥ −54
Answer: x ≥ −9
- Divide both sides by 6 (positive, so the sign stays): x ≥ −9
5.3x ≤ 15
Answer: x ≤ 5
- Divide both sides by 3 (positive, so the sign stays): x ≤ 5
6.4x ≥ 36
Answer: x ≥ 9
- Divide both sides by 4 (positive, so the sign stays): x ≥ 9
7.x + 6 < 3
Answer: x < −3
- Subtract 6 on both sides: x < 3 − 6 = −3
8.x − 1 < −8
Answer: x < −7
- Add 1 on both sides: x < −8 + 1 = −7
9.9x > 27
Answer: x > 3
- Divide both sides by 9 (positive, so the sign stays): x > 3
10.x + 4 ≤ 13
Answer: x ≤ 9
- Subtract 4 on both sides: x ≤ 13 − 4 = 9
11.5x ≥ 20
Answer: x ≥ 4
- Divide both sides by 5 (positive, so the sign stays): x ≥ 4
12.x + 4 ≥ 12
Answer: x ≥ 8
- Subtract 4 on both sides: x ≥ 12 − 4 = 8
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.