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.
1.7x ≤ 35
Answer: x ≤ 5
- Divide both sides by 7 (positive, so the sign stays): x ≤ 5
2.x + 8 ≤ 10
Answer: x ≤ 2
- Subtract 8 on both sides: x ≤ 10 − 8 = 2
3.x − 8 > −12
Answer: x > −4
- Add 8 on both sides: x > −12 + 8 = −4
4.x + 7 > −1
Answer: x > −8
- Subtract 7 on both sides: x > −1 − 7 = −8
5.x + 8 < 19
Answer: x < 11
- Subtract 8 on both sides: x < 19 − 8 = 11
6.x + 5 ≥ −3
Answer: x ≥ −8
- Subtract 5 on both sides: x ≥ −3 − 5 = −8
7.x + 6 ≤ 3
Answer: x ≤ −3
- Subtract 6 on both sides: x ≤ 3 − 6 = −3
8.x − 8 > −5
Answer: x > 3
- Add 8 on both sides: x > −5 + 8 = 3
9.5x ≥ −20
Answer: x ≥ −4
- Divide both sides by 5 (positive, so the sign stays): x ≥ −4
10.9x ≥ −27
Answer: x ≥ −3
- Divide both sides by 9 (positive, so the sign stays): x ≥ −3
11.x + 6 < −1
Answer: x < −7
- Subtract 6 on both sides: x < −1 − 6 = −7
12.x − 2 > 3
Answer: x > 5
- Add 2 on both sides: x > 3 + 2 = 5
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.