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 + 8 < −28
Answer: x < −6
- Subtract 8: 6x < −36
- Divide by 6: x < −6
2.Solve: 5x + 7 < 7
Answer: x < 0
- Subtract 7: 5x < 0
- Divide by 5: x < 0
3.Solve: 6x + 1 ≤ −5
Answer: x ≤ −1
- Subtract 1: 6x ≤ −6
- Divide by 6: x ≤ −1
4.Solve: 2x + 2 < 20
Answer: x < 9
- Subtract 2: 2x < 18
- Divide by 2: x < 9
5.Solve: 6x + 3 ≤ −15
Answer: x ≤ −3
- Subtract 3: 6x ≤ −18
- Divide by 6: x ≤ −3
6.Solve: 6x + 4 ≥ −26
Answer: x ≥ −5
- Subtract 4: 6x ≥ −30
- Divide by 6: x ≥ −5
7.Solve: 4x + 1 > −31
Answer: x > −8
- Subtract 1: 4x > −32
- Divide by 4: x > −8
8.Solve: 4x + 9 ≥ 13
Answer: x ≥ 1
- Subtract 9: 4x ≥ 4
- Divide by 4: x ≥ 1
9.Solve: 7x + 7 ≥ 70
Answer: x ≥ 9
- Subtract 7: 7x ≥ 63
- Divide by 7: x ≥ 9
10.Solve: 7x − 9 > 47
Answer: x > 8
- Add 9: 7x > 56
- Divide by 7: x > 8
11.Solve: 4x + 11 > 43
Answer: x > 8
- Subtract 11: 4x > 32
- Divide by 4: x > 8
12.Solve: 7x − 7 < −14
Answer: x < −1
- Add 7: 7x < −7
- Divide by 7: x < −1
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.