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: 7x − 1 > 41
Answer: x > 6
- Add 1: 7x > 42
- Divide by 7: x > 6
2.Solve: 6x + 7 ≤ 43
Answer: x ≤ 6
- Subtract 7: 6x ≤ 36
- Divide by 6: x ≤ 6
3.Solve: 3x − 5 < 13
Answer: x < 6
- Add 5: 3x < 18
- Divide by 3: x < 6
4.Solve: 6x − 11 ≥ −11
Answer: x ≥ 0
- Add 11: 6x ≥ 0
- Divide by 6: x ≥ 0
5.Solve: 6x − 10 ≥ −52
Answer: x ≥ −7
- Add 10: 6x ≥ −42
- Divide by 6: x ≥ −7
6.Solve: 2x − 3 < 5
Answer: x < 4
- Add 3: 2x < 8
- Divide by 2: x < 4
7.Solve: 7x + 1 ≥ 22
Answer: x ≥ 3
- Subtract 1: 7x ≥ 21
- Divide by 7: x ≥ 3
8.Solve: 3x − 9 ≤ −3
Answer: x ≤ 2
- Add 9: 3x ≤ 6
- Divide by 3: x ≤ 2
9.Solve: 5x + 3 ≤ 18
Answer: x ≤ 3
- Subtract 3: 5x ≤ 15
- Divide by 5: x ≤ 3
10.Solve: 6x − 5 ≤ −41
Answer: x ≤ −6
- Add 5: 6x ≤ −36
- Divide by 6: x ≤ −6
11.Solve: 3x − 2 ≤ 28
Answer: x ≤ 10
- Add 2: 3x ≤ 30
- Divide by 3: x ≤ 10
12.Solve: 2x + 7 > −3
Answer: x > −5
- Subtract 7: 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.