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.x + 9 ≥ 13
Answer: x ≥ 4
- Subtract 9 on both sides: x ≥ 13 − 9 = 4
2.x − 2 ≤ 3
Answer: x ≤ 5
- Add 2 on both sides: x ≤ 3 + 2 = 5
3.6x < 54
Answer: x < 9
- Divide both sides by 6 (positive, so the sign stays): x < 9
4.x + 2 > 2
Answer: x > 0
- Subtract 2 on both sides: x > 2 − 2 = 0
5.3x ≥ 0
Answer: x ≥ 0
- Divide both sides by 3 (positive, so the sign stays): x ≥ 0
6.x − 6 ≤ −8
Answer: x ≤ −2
- Add 6 on both sides: x ≤ −8 + 6 = −2
7.x − 5 ≥ −2
Answer: x ≥ 3
- Add 5 on both sides: x ≥ −2 + 5 = 3
8.x + 4 ≥ 4
Answer: x ≥ 0
- Subtract 4 on both sides: x ≥ 4 − 4 = 0
9.x − 2 < 5
Answer: x < 7
- Add 2 on both sides: x < 5 + 2 = 7
10.x + 3 > 5
Answer: x > 2
- Subtract 3 on both sides: x > 5 − 3 = 2
11.x − 3 > 8
Answer: x > 11
- Add 3 on both sides: x > 8 + 3 = 11
12.9x < 108
Answer: x < 12
- Divide both sides by 9 (positive, so the sign stays): x < 12
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.