Year 9 Solving Linear Inequalities Worksheet — Level 1 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 9 linear equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Linear EquationsYear 9 Solving Linear Inequalities Worksheet — Level 1 — Practice Set 4 — Answers
Solve each inequality the same way you would solve an equation.
1.4x ≤ 32
Answer: x ≤ 8
- Divide both sides by 4 (positive, so the sign stays): x ≤ 8
2.x − 4 < 3
Answer: x < 7
- Add 4 on both sides: x < 3 + 4 = 7
3.x + 7 ≥ 12
Answer: x ≥ 5
- Subtract 7 on both sides: x ≥ 12 − 7 = 5
4.3x ≤ −9
Answer: x ≤ −3
- Divide both sides by 3 (positive, so the sign stays): x ≤ −3
5.2x ≥ 2
Answer: x ≥ 1
- Divide both sides by 2 (positive, so the sign stays): x ≥ 1
6.2x ≤ 18
Answer: x ≤ 9
- Divide both sides by 2 (positive, so the sign stays): x ≤ 9
7.x + 4 ≥ 6
Answer: x ≥ 2
- Subtract 4 on both sides: x ≥ 6 − 4 = 2
8.3x > 12
Answer: x > 4
- Divide both sides by 3 (positive, so the sign stays): x > 4
9.3x > 18
Answer: x > 6
- Divide both sides by 3 (positive, so the sign stays): x > 6
10.x + 4 ≥ −2
Answer: x ≥ −6
- Subtract 4 on both sides: x ≥ −2 − 4 = −6
11.2x > −12
Answer: x > −6
- Divide both sides by 2 (positive, so the sign stays): x > −6
12.x − 3 ≥ −9
Answer: x ≥ −6
- Add 3 on both sides: x ≥ −9 + 3 = −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.
- Celebrate what went well first, then pick one thing to work on next.