Year 9 Solving Linear Inequalities Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 9 linear equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Linear EquationsYear 9 Solving Linear Inequalities Worksheet — Level 3 — Answers
Solve each inequality. When you multiply or divide both sides by a negative number, reverse the inequality sign.
1.Solve: 4x − 1 > 47
Answer: x > 12
- Add 1: 4x > 48
- Divide by 4: x > 12
2.Solve: 6x + 5 > 29
Answer: x > 4
- Subtract 5: 6x > 24
- Divide by 6: x > 4
3.Solve: 4x + 3 > 43
Answer: x > 10
- Subtract 3: 4x > 40
- Divide by 4: x > 10
4.Solve: 5x + 9 ≤ 54
Answer: x ≤ 9
- Subtract 9: 5x ≤ 45
- Divide by 5: x ≤ 9
5.Solve: −6x − 8 < 34
Answer: x > −7
- Add 8: −6x < 42
- Divide by −6 (negative, so reverse the sign): x > −7
6.Solve: 4x − 5 < 39
Answer: x < 11
- Add 5: 4x < 44
- Divide by 4: x < 11
7.Solve: −6x − 12 ≤ −84
Answer: x ≥ 12
- Add 12: −6x ≤ −72
- Divide by −6 (negative, so reverse the sign): x ≥ 12
8.Solve: −x + 8 ≤ 15
Answer: x ≥ −7
- Subtract 8: −x ≤ 7
- Divide by −1 (negative, so reverse the sign): x ≥ −7
9.Solve: 4x + 9 ≤ 25
Answer: x ≤ 4
- Subtract 9: 4x ≤ 16
- Divide by 4: x ≤ 4
10.Solve: 2x − 8 ≥ −18
Answer: x ≥ −5
- Add 8: 2x ≥ −10
- Divide by 2: x ≥ −5
11.Solve: −x − 8 > −10
Answer: x < 2
- Add 8: −x > −2
- Divide by −1 (negative, so reverse the sign): x < 2
12.Solve: 4x + 4 ≥ −12
Answer: x ≥ −4
- Subtract 4: 4x ≥ −16
- Divide by 4: x ≥ −4
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.