Inequalities — O/L Mathematics

How do I practise Inequalities?

2 questions with worked solutions

1. Solve the compound linear inequality: -3 ≤ 2x + 1 < 9, where x ∈ ℝ.
   1. A) -1 ≤ x < 5
   2. B) -4 ≤ x < 8
   3. C) -2 < x ≤ 4
   4. D) -2 ≤ x < 4
   Check my answer

   Correct answer: D) -2 ≤ x < 4

   Subtract 1 from all parts: -3 - 1 ≤ 2x < 9 - 1 → -4 ≤ 2x < 8. Divide by 2: -2 ≤ x < 4.

   Show worked solution

   Step 1: Start with -3 ≤ 2x + 1 < 9. Step 2: Subtract 1 throughout: -4 ≤ 2x < 8. Step 3: Divide entire inequality by positive 2 (inequality signs remain unchanged): -2 ≤ x < 4. Answer: -2 ≤ x < 4.
   Modelled on: the O/L Mathematics examination pattern
2. Solve the inequality 3(x - 2) > 5x + 4, where x ∈ ℝ.
   1. A) x < -5
   2. B) x > -5
   3. C) x > 5
   4. D) x < 5
   Check my answer

   Correct answer: A) x < -5

   Expanding gives 3x - 6 > 5x + 4. Collecting terms, -2x > 10. Dividing by -2 reverses the inequality sign, so x < -5.

   Show worked solution

   Step 1: Expand the bracket: 3x - 6 > 5x + 4. Step 2: Subtract 5x from both sides: -2x - 6 > 4. Step 3: Add 6 to both sides: -2x > 10. Step 4: Divide both sides by -2 and reverse the inequality sign: x < -5. Answer: x < -5.
   Modelled on: the O/L Mathematics examination pattern

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Where does Inequalities fit in the syllabus?

Grade 11 · Term 3