Grade 10 Maths · Algebra

Solve a linear inequality

Solve an inequality like an equation, but flip the sign when you multiply or divide by a negative (for example −2x > 6 gives x < −3).

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Inequality Exam Grade 10Kevinmathscience

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Question 2.2 · March 2024 · Provincial · 4 marks

2.2 Solve the inequality

- 2 < 4 + 2 x \leq 6

and represent the solution in interval notation.(4)

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More past paper questions: solve a linear inequality

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3. Question 2.3.1 · March 2025 · Provincial · 2 marks
2.3 Given: $- 9 \leq - 2 x + 3 < 5$
2.3.1 Solve for x.(2)
Show the memo (2 ticks)Memo
1. ✓
  Subtract 3 $- 12 \leq - 2 x < 2$
  1 mark · Solve a linear inequality
2. ✓
  Divide by -2 and flip signs $6 \geq x > - 1$ (or $- 1 < x \leq 6$ )
  1 mark · Solve a linear inequality
4. Question 3.2.1 · June 2024 · Paper 1 · Provincial · 2 marks
3.2 Given: $2 - \frac{3 x}{4} < 14$
3.2.1 Solve the inequality.(2)
Show the memo (2 ticks)Memo
1. ✓
  Isolate the term with x $- \frac{3 x}{4} < 12$
  1 mark · Solve a linear inequality
2. ✓
  Solve for x (reversing inequality sign) $x > 12 \times (- \frac{4}{3})$
  $x > - 16$
  1 mark · Solve a linear inequality
5. Question 2.2.1 · March 2020 · Provincial · 3 marks
2.2 Inequality analysis:
2.2.1 Solve for x: $- 11 < - 2 x + 1 < - 9$ ; $x \in R$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Isolate variable term $- 12 < - 2 x < - 10$
  1 mark · Solve a linear inequality
2. ✓
  Divide by -2 (flip inequality) $6 > x > 5 ⟹ 5 < x < 6$
  2 marks · Solve a linear inequality
6. Question 4.2.1 · March 2019 · Provincial · 3 marks
4.2 The following inequality is given: $- 9 \leq 2 x + 3 < 5$ where $x \in R$
4.2.1 Solve for $x$ in the inequality.(3)
Show the memo (2 ticks)Memo
1. ✓
  Subtract 3 from all sides $- 12 \leq 2 x < 2$
  1 mark · Solve a linear inequality
2. ✓
  Divide by 2 $- 6 \leq x < 1$
  2 marks · Solve a linear inequality

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