Year 8 Solving Linear Inequalities Worksheet — Level 3 — 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 3 — Practice Set 4 — Answers
Solve each inequality. When you multiply or divide both sides by a negative number, reverse the inequality sign.
1.Solve: 2x + 3 < 27
Answer: x < 12
- Subtract 3: 2x < 24
- Divide by 2: x < 12
2.Solve: 3x + 4 ≤ −11
Answer: x ≤ −5
- Subtract 4: 3x ≤ −15
- Divide by 3: x ≤ −5
3.Solve: 2x + 11 < 35
Answer: x < 12
- Subtract 11: 2x < 24
- Divide by 2: x < 12
4.Solve: 6x + 5 ≥ 65
Answer: x ≥ 10
- Subtract 5: 6x ≥ 60
- Divide by 6: x ≥ 10
5.Solve: −5x + 12 ≤ 37
Answer: x ≥ −5
- Subtract 12: −5x ≤ 25
- Divide by −5 (negative, so reverse the sign): x ≥ −5
6.Solve: −2x + 3 ≤ −19
Answer: x ≥ 11
- Subtract 3: −2x ≤ −22
- Divide by −2 (negative, so reverse the sign): x ≥ 11
7.Solve: x − 11 < −13
Answer: x < −2
- Add 11: x < −2
- Divide by 1: x < −2
8.Solve: x − 12 ≥ −7
Answer: x ≥ 5
- Add 12: x ≥ 5
- Divide by 1: x ≥ 5
9.Solve: x + 7 ≤ 2
Answer: x ≤ −5
- Subtract 7: x ≤ −5
- Divide by 1: x ≤ −5
10.Solve: 3x + 12 ≤ 0
Answer: x ≤ −4
- Subtract 12: 3x ≤ −12
- Divide by 3: x ≤ −4
11.Solve: x − 8 > 2
Answer: x > 10
- Add 8: x > 10
- Divide by 1: x > 10
12.Solve: 3x + 1 ≥ 16
Answer: x ≥ 5
- Subtract 1: 3x ≥ 15
- Divide by 3: 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.