Year 9 Solving Linear Inequalities Worksheet — Level 2 — Practice Set 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 2 — Practice Set 3 — Answers
Solve each inequality the same way you would solve an equation.
1.Solve: 6x − 2 < −32
Answer: x < −5
- Add 2: 6x < −30
- Divide by 6: x < −5
2.Solve: 6x + 12 < −30
Answer: x < −7
- Subtract 12: 6x < −42
- Divide by 6: x < −7
3.Solve: 6x − 7 ≥ −49
Answer: x ≥ −7
- Add 7: 6x ≥ −42
- Divide by 6: x ≥ −7
4.Solve: 4x + 4 ≥ 40
Answer: x ≥ 9
- Subtract 4: 4x ≥ 36
- Divide by 4: x ≥ 9
5.Solve: 6x − 1 < −49
Answer: x < −8
- Add 1: 6x < −48
- Divide by 6: x < −8
6.Solve: 7x − 12 < 44
Answer: x < 8
- Add 12: 7x < 56
- Divide by 7: x < 8
7.Solve: 7x − 2 > 54
Answer: x > 8
- Add 2: 7x > 56
- Divide by 7: x > 8
8.Solve: 6x + 9 ≤ −45
Answer: x ≤ −9
- Subtract 9: 6x ≤ −54
- Divide by 6: x ≤ −9
9.Solve: 7x − 9 > 12
Answer: x > 3
- Add 9: 7x > 21
- Divide by 7: x > 3
10.Solve: 4x − 7 ≥ 13
Answer: x ≥ 5
- Add 7: 4x ≥ 20
- Divide by 4: x ≥ 5
11.Solve: 4x − 7 ≤ 37
Answer: x ≤ 11
- Add 7: 4x ≤ 44
- Divide by 4: x ≤ 11
12.Solve: 3x − 2 < 25
Answer: x < 9
- Add 2: 3x < 27
- Divide by 3: x < 9
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.