Year 8 Solving Linear Inequalities Worksheet — Level 1 — 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 — Answers
Solve each inequality the same way you would solve an equation.
1.x + 7 ≥ 8
Answer: x ≥ 1
- Subtract 7 on both sides: x ≥ 8 − 7 = 1
2.x + 5 ≤ 7
Answer: x ≤ 2
- Subtract 5 on both sides: x ≤ 7 − 5 = 2
3.x − 8 < 2
Answer: x < 10
- Add 8 on both sides: x < 2 + 8 = 10
4.3x > 33
Answer: x > 11
- Divide both sides by 3 (positive, so the sign stays): x > 11
5.x − 9 > 3
Answer: x > 12
- Add 9 on both sides: x > 3 + 9 = 12
6.x − 5 > −14
Answer: x > −9
- Add 5 on both sides: x > −14 + 5 = −9
7.3x < −27
Answer: x < −9
- Divide both sides by 3 (positive, so the sign stays): x < −9
8.2x < 22
Answer: x < 11
- Divide both sides by 2 (positive, so the sign stays): x < 11
9.8x ≤ 32
Answer: x ≤ 4
- Divide both sides by 8 (positive, so the sign stays): x ≤ 4
10.x − 4 > −10
Answer: x > −6
- Add 4 on both sides: x > −10 + 4 = −6
11.5x ≤ 40
Answer: x ≤ 8
- Divide both sides by 5 (positive, so the sign stays): x ≤ 8
12.9x ≤ 0
Answer: x ≤ 0
- Divide both sides by 9 (positive, so the sign stays): x ≤ 0
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.