Year 10 Solving Linear Inequalities Worksheet — Level 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 3 — Answers
Solve each inequality. When you multiply or divide both sides by a negative number, reverse the inequality sign.
1.Solve: 4x − 9 ≤ −25
Answer: x ≤ −4
- Add 9: 4x ≤ −16
- Divide by 4: x ≤ −4
2.Solve: −3x − 5 < −8
Answer: x > 1
- Add 5: −3x < −3
- Divide by −3 (negative, so reverse the sign): x > 1
3.Solve: 4x + 1 ≥ 41
Answer: x ≥ 10
- Subtract 1: 4x ≥ 40
- Divide by 4: x ≥ 10
4.Solve: 4x − 7 ≥ −31
Answer: x ≥ −6
- Add 7: 4x ≥ −24
- Divide by 4: x ≥ −6
5.Solve: 5x + 12 < 47
Answer: x < 7
- Subtract 12: 5x < 35
- Divide by 5: x < 7
6.Solve: 5x − 9 ≥ 36
Answer: x ≥ 9
- Add 9: 5x ≥ 45
- Divide by 5: x ≥ 9
7.Solve: −2x + 3 ≥ −15
Answer: x ≤ 9
- Subtract 3: −2x ≥ −18
- Divide by −2 (negative, so reverse the sign): x ≤ 9
8.Solve: x − 6 ≥ −5
Answer: x ≥ 1
- Add 6: x ≥ 1
- Divide by 1: x ≥ 1
9.Solve: −2x − 8 ≤ −6
Answer: x ≥ −1
- Add 8: −2x ≤ 2
- Divide by −2 (negative, so reverse the sign): x ≥ −1
10.Solve: 6x + 6 ≤ 0
Answer: x ≤ −1
- Subtract 6: 6x ≤ −6
- Divide by 6: x ≤ −1
11.Solve: −5x + 11 < 31
Answer: x > −4
- Subtract 11: −5x < 20
- Divide by −5 (negative, so reverse the sign): x > −4
12.Solve: 3x − 2 ≥ 16
Answer: x ≥ 6
- Add 2: 3x ≥ 18
- Divide by 3: x ≥ 6
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