Year 8 Solving Linear Inequalities Worksheet — Level 2 — Practice Set 4 — 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 4 — Answers
Solve each inequality the same way you would solve an equation.
1.Solve: 4x − 6 ≤ 18
Answer: x ≤ 6
- Add 6: 4x ≤ 24
- Divide by 4: x ≤ 6
2.Solve: 6x − 1 < 41
Answer: x < 7
- Add 1: 6x < 42
- Divide by 6: x < 7
3.Solve: 2x − 7 > −13
Answer: x > −3
- Add 7: 2x > −6
- Divide by 2: x > −3
4.Solve: 5x + 2 ≤ 22
Answer: x ≤ 4
- Subtract 2: 5x ≤ 20
- Divide by 5: x ≤ 4
5.Solve: 2x + 3 < 15
Answer: x < 6
- Subtract 3: 2x < 12
- Divide by 2: x < 6
6.Solve: 5x + 3 > −17
Answer: x > −4
- Subtract 3: 5x > −20
- Divide by 5: x > −4
7.Solve: 4x + 4 ≤ 24
Answer: x ≤ 5
- Subtract 4: 4x ≤ 20
- Divide by 4: x ≤ 5
8.Solve: 3x + 8 ≥ 44
Answer: x ≥ 12
- Subtract 8: 3x ≥ 36
- Divide by 3: x ≥ 12
9.Solve: 7x + 3 ≤ 73
Answer: x ≤ 10
- Subtract 3: 7x ≤ 70
- Divide by 7: x ≤ 10
10.Solve: 3x − 3 < 3
Answer: x < 2
- Add 3: 3x < 6
- Divide by 3: x < 2
11.Solve: 6x − 12 < 48
Answer: x < 10
- Add 12: 6x < 60
- Divide by 6: x < 10
12.Solve: 3x − 1 > 5
Answer: x > 2
- Add 1: 3x > 6
- Divide by 3: x > 2
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.