Year 7 Solving Linear Inequalities Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 7 linear equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 7 · Mathematics · Linear EquationsYear 7 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: −3x − 8 ≤ 13
Answer: x ≥ −7
- Add 8: −3x ≤ 21
- Divide by −3 (negative, so reverse the sign): x ≥ −7
2.Solve: x + 5 ≥ 12
Answer: x ≥ 7
- Subtract 5: x ≥ 7
- Divide by 1: x ≥ 7
3.Solve: x + 7 ≤ 17
Answer: x ≤ 10
- Subtract 7: x ≤ 10
- Divide by 1: x ≤ 10
4.Solve: 3x + 7 ≥ 16
Answer: x ≥ 3
- Subtract 7: 3x ≥ 9
- Divide by 3: x ≥ 3
5.Solve: 6x − 7 ≥ −37
Answer: x ≥ −5
- Add 7: 6x ≥ −30
- Divide by 6: x ≥ −5
6.Solve: −4x + 5 ≥ 17
Answer: x ≤ −3
- Subtract 5: −4x ≥ 12
- Divide by −4 (negative, so reverse the sign): x ≤ −3
7.Solve: 6x + 3 ≥ 33
Answer: x ≥ 5
- Subtract 3: 6x ≥ 30
- Divide by 6: x ≥ 5
8.Solve: 6x + 11 ≥ 23
Answer: x ≥ 2
- Subtract 11: 6x ≥ 12
- Divide by 6: x ≥ 2
9.Solve: −x + 10 < 12
Answer: x > −2
- Subtract 10: −x < 2
- Divide by −1 (negative, so reverse the sign): x > −2
10.Solve: −x − 11 ≥ −3
Answer: x ≤ −8
- Add 11: −x ≥ 8
- Divide by −1 (negative, so reverse the sign): x ≤ −8
11.Solve: 6x + 3 ≤ 15
Answer: x ≤ 2
- Subtract 3: 6x ≤ 12
- Divide by 6: x ≤ 2
12.Solve: 4x + 5 ≥ 33
Answer: x ≥ 7
- Subtract 5: 4x ≥ 28
- Divide by 4: x ≥ 7
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
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