Year 10 Solving Linear Inequalities Worksheet — Level 2 — Practice Set 4 — 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 4 — Answers
Solve each inequality the same way you would solve an equation.
1.Solve: 7x − 7 ≥ −42
Answer: x ≥ −5
- Add 7: 7x ≥ −35
- Divide by 7: x ≥ −5
2.Solve: 2x − 2 ≥ 4
Answer: x ≥ 3
- Add 2: 2x ≥ 6
- Divide by 2: x ≥ 3
3.Solve: 7x + 3 ≥ 52
Answer: x ≥ 7
- Subtract 3: 7x ≥ 49
- Divide by 7: x ≥ 7
4.Solve: 2x − 10 > −8
Answer: x > 1
- Add 10: 2x > 2
- Divide by 2: x > 1
5.Solve: 2x + 6 ≥ 4
Answer: x ≥ −1
- Subtract 6: 2x ≥ −2
- Divide by 2: x ≥ −1
6.Solve: 4x + 1 ≤ 37
Answer: x ≤ 9
- Subtract 1: 4x ≤ 36
- Divide by 4: x ≤ 9
7.Solve: 4x − 6 > 30
Answer: x > 9
- Add 6: 4x > 36
- Divide by 4: x > 9
8.Solve: 5x + 1 ≤ 21
Answer: x ≤ 4
- Subtract 1: 5x ≤ 20
- Divide by 5: x ≤ 4
9.Solve: 4x + 11 < 27
Answer: x < 4
- Subtract 11: 4x < 16
- Divide by 4: x < 4
10.Solve: 2x + 10 < 30
Answer: x < 10
- Subtract 10: 2x < 20
- Divide by 2: x < 10
11.Solve: 3x + 1 ≤ 7
Answer: x ≤ 2
- Subtract 1: 3x ≤ 6
- Divide by 3: x ≤ 2
12.Solve: 5x − 5 < 15
Answer: x < 4
- Add 5: 5x < 20
- Divide by 5: 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.