Year 10 Solving Linear Inequalities Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 10 linear equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Linear EquationsYear 10 Solving Linear Inequalities Worksheet — Level 2 — Practice Set 3 — Answers
Solve each inequality the same way you would solve an equation.
1.Solve: 6x − 12 ≤ −24
Answer: x ≤ −2
- Add 12: 6x ≤ −12
- Divide by 6: x ≤ −2
2.Solve: 4x + 10 < 30
Answer: x < 5
- Subtract 10: 4x < 20
- Divide by 4: x < 5
3.Solve: 5x + 4 ≥ 49
Answer: x ≥ 9
- Subtract 4: 5x ≥ 45
- Divide by 5: x ≥ 9
4.Solve: 4x − 10 > 34
Answer: x > 11
- Add 10: 4x > 44
- Divide by 4: x > 11
5.Solve: 2x − 2 < 20
Answer: x < 11
- Add 2: 2x < 22
- Divide by 2: x < 11
6.Solve: 7x − 8 ≤ −50
Answer: x ≤ −6
- Add 8: 7x ≤ −42
- Divide by 7: x ≤ −6
7.Solve: 7x − 3 < −45
Answer: x < −6
- Add 3: 7x < −42
- Divide by 7: x < −6
8.Solve: 7x + 2 ≥ 30
Answer: x ≥ 4
- Subtract 2: 7x ≥ 28
- Divide by 7: x ≥ 4
9.Solve: 5x − 3 ≥ 22
Answer: x ≥ 5
- Add 3: 5x ≥ 25
- Divide by 5: x ≥ 5
10.Solve: 2x + 5 < 19
Answer: x < 7
- Subtract 5: 2x < 14
- Divide by 2: x < 7
11.Solve: 7x − 4 > −46
Answer: x > −6
- Add 4: 7x > −42
- Divide by 7: x > −6
12.Solve: 2x + 12 < 2
Answer: x < −5
- Subtract 12: 2x < −10
- Divide by 2: 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.