Year 8 Solving Linear Inequalities Worksheet — Level 3 — 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 3 — Practice Set 3 — Answers
Solve each inequality. When you multiply or divide both sides by a negative number, reverse the inequality sign.
1.Solve: x + 8 > 1
Answer: x > −7
- Subtract 8: x > −7
- Divide by 1: x > −7
2.Solve: 6x + 4 ≤ −44
Answer: x ≤ −8
- Subtract 4: 6x ≤ −48
- Divide by 6: x ≤ −8
3.Solve: 2x − 4 ≥ 2
Answer: x ≥ 3
- Add 4: 2x ≥ 6
- Divide by 2: x ≥ 3
4.Solve: 4x + 12 < −24
Answer: x < −9
- Subtract 12: 4x < −36
- Divide by 4: x < −9
5.Solve: 2x + 6 < −4
Answer: x < −5
- Subtract 6: 2x < −10
- Divide by 2: x < −5
6.Solve: 6x + 8 > 44
Answer: x > 6
- Subtract 8: 6x > 36
- Divide by 6: x > 6
7.Solve: 4x + 5 ≤ 21
Answer: x ≤ 4
- Subtract 5: 4x ≤ 16
- Divide by 4: x ≤ 4
8.Solve: 3x + 6 ≥ −21
Answer: x ≥ −9
- Subtract 6: 3x ≥ −27
- Divide by 3: x ≥ −9
9.Solve: −4x + 10 ≤ 2
Answer: x ≥ 2
- Subtract 10: −4x ≤ −8
- Divide by −4 (negative, so reverse the sign): x ≥ 2
10.Solve: 5x + 3 > 53
Answer: x > 10
- Subtract 3: 5x > 50
- Divide by 5: x > 10
11.Solve: 3x + 12 ≥ −9
Answer: x ≥ −7
- Subtract 12: 3x ≥ −21
- Divide by 3: x ≥ −7
12.Solve: 2x − 3 ≥ 17
Answer: x ≥ 10
- Add 3: 2x ≥ 20
- Divide by 2: x ≥ 10
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.
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