Year 7 Solving Linear Inequalities Worksheet — Level 1 — Answers
Answer sheet with worked solutions for the Year 7 linear equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 7 · Mathematics · Linear EquationsYear 7 Solving Linear Inequalities Worksheet — Level 1 — Answers
Solve each inequality the same way you would solve an equation.
1.x − 4 ≤ −4
Answer: x ≤ 0
- Add 4 on both sides: x ≤ −4 + 4 = 0
2.x − 9 < −12
Answer: x < −3
- Add 9 on both sides: x < −12 + 9 = −3
3.x + 5 ≤ 12
Answer: x ≤ 7
- Subtract 5 on both sides: x ≤ 12 − 5 = 7
4.x − 6 ≥ −10
Answer: x ≥ −4
- Add 6 on both sides: x ≥ −10 + 6 = −4
5.3x ≤ 30
Answer: x ≤ 10
- Divide both sides by 3 (positive, so the sign stays): x ≤ 10
6.x + 5 ≥ 4
Answer: x ≥ −1
- Subtract 5 on both sides: x ≥ 4 − 5 = −1
7.x − 1 ≥ 7
Answer: x ≥ 8
- Add 1 on both sides: x ≥ 7 + 1 = 8
8.x − 8 ≥ −10
Answer: x ≥ −2
- Add 8 on both sides: x ≥ −10 + 8 = −2
9.x − 8 < 2
Answer: x < 10
- Add 8 on both sides: x < 2 + 8 = 10
10.x − 7 < 1
Answer: x < 8
- Add 7 on both sides: x < 1 + 7 = 8
11.5x < −35
Answer: x < −7
- Divide both sides by 5 (positive, so the sign stays): x < −7
12.x − 3 ≤ −10
Answer: x ≤ −7
- Add 3 on both sides: x ≤ −10 + 3 = −7
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.