Year 8 Solving Linear Inequalities Worksheet — Level 2 — 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 2 — Practice Set 3 — Answers
Solve each inequality the same way you would solve an equation.
1.Solve: 6x − 11 > 1
Answer: x > 2
- Add 11: 6x > 12
- Divide by 6: x > 2
2.Solve: 7x + 12 ≤ 75
Answer: x ≤ 9
- Subtract 12: 7x ≤ 63
- Divide by 7: x ≤ 9
3.Solve: 3x − 7 < −25
Answer: x < −6
- Add 7: 3x < −18
- Divide by 3: x < −6
4.Solve: 5x + 6 < 61
Answer: x < 11
- Subtract 6: 5x < 55
- Divide by 5: x < 11
5.Solve: 3x + 12 ≤ 15
Answer: x ≤ 1
- Subtract 12: 3x ≤ 3
- Divide by 3: x ≤ 1
6.Solve: 5x + 4 < −1
Answer: x < −1
- Subtract 4: 5x < −5
- Divide by 5: x < −1
7.Solve: 5x + 9 < 54
Answer: x < 9
- Subtract 9: 5x < 45
- Divide by 5: x < 9
8.Solve: 5x + 7 ≥ 22
Answer: x ≥ 3
- Subtract 7: 5x ≥ 15
- Divide by 5: x ≥ 3
9.Solve: 4x − 1 < 3
Answer: x < 1
- Add 1: 4x < 4
- Divide by 4: x < 1
10.Solve: 4x − 4 < −20
Answer: x < −4
- Add 4: 4x < −16
- Divide by 4: x < −4
11.Solve: 3x + 8 > 26
Answer: x > 6
- Subtract 8: 3x > 18
- Divide by 3: x > 6
12.Solve: 5x − 7 ≤ −32
Answer: x ≤ −5
- Add 7: 5x ≤ −25
- Divide by 5: x ≤ −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.