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.
1.7x ≤ 56
Answer: x ≤ 8
- Divide both sides by 7 (positive, so the sign stays): x ≤ 8
2.x + 2 ≥ 14
Answer: x ≥ 12
- Subtract 2 on both sides: x ≥ 14 − 2 = 12
3.x − 5 ≥ 5
Answer: x ≥ 10
- Add 5 on both sides: x ≥ 5 + 5 = 10
4.x + 9 ≤ 17
Answer: x ≤ 8
- Subtract 9 on both sides: x ≤ 17 − 9 = 8
5.2x ≥ 2
Answer: x ≥ 1
- Divide both sides by 2 (positive, so the sign stays): x ≥ 1
6.5x ≤ 15
Answer: x ≤ 3
- Divide both sides by 5 (positive, so the sign stays): x ≤ 3
7.7x < 77
Answer: x < 11
- Divide both sides by 7 (positive, so the sign stays): x < 11
8.x + 2 < 2
Answer: x < 0
- Subtract 2 on both sides: x < 2 − 2 = 0
9.8x > −24
Answer: x > −3
- Divide both sides by 8 (positive, so the sign stays): x > −3
10.8x ≤ 64
Answer: x ≤ 8
- Divide both sides by 8 (positive, so the sign stays): x ≤ 8
11.x + 7 > 12
Answer: x > 5
- Subtract 7 on both sides: x > 12 − 7 = 5
12.x + 9 ≤ 0
Answer: x ≤ −9
- Subtract 9 on both sides: x ≤ 0 − 9 = −9
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.