Year 7 Solving Linear Inequalities Worksheet — Level 2 — Practice Set 2 — 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 2 — Practice Set 2 — Answers
Solve each inequality the same way you would solve an equation.
1.Solve: 3x + 1 ≤ 1
Answer: x ≤ 0
- Subtract 1: 3x ≤ 0
- Divide by 3: x ≤ 0
2.Solve: 2x − 6 ≤ −6
Answer: x ≤ 0
- Add 6: 2x ≤ 0
- Divide by 2: x ≤ 0
3.Solve: 2x + 12 < 36
Answer: x < 12
- Subtract 12: 2x < 24
- Divide by 2: x < 12
4.Solve: 2x − 12 ≤ −20
Answer: x ≤ −4
- Add 12: 2x ≤ −8
- Divide by 2: x ≤ −4
5.Solve: 6x − 12 ≤ −42
Answer: x ≤ −5
- Add 12: 6x ≤ −30
- Divide by 6: x ≤ −5
6.Solve: 5x + 12 ≥ 62
Answer: x ≥ 10
- Subtract 12: 5x ≥ 50
- Divide by 5: x ≥ 10
7.Solve: 5x − 1 < 34
Answer: x < 7
- Add 1: 5x < 35
- Divide by 5: x < 7
8.Solve: 4x + 8 ≤ 16
Answer: x ≤ 2
- Subtract 8: 4x ≤ 8
- Divide by 4: x ≤ 2
9.Solve: 6x + 7 ≥ −17
Answer: x ≥ −4
- Subtract 7: 6x ≥ −24
- Divide by 6: x ≥ −4
10.Solve: 3x + 1 > 16
Answer: x > 5
- Subtract 1: 3x > 15
- Divide by 3: x > 5
11.Solve: 2x − 12 > −18
Answer: x > −3
- Add 12: 2x > −6
- Divide by 2: x > −3
12.Solve: 6x − 9 < −57
Answer: x < −8
- Add 9: 6x < −48
- Divide by 6: x < −8
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.