Linear Inequalities — O/L Mathematics

How do I practise Linear Inequalities?

2 questions with worked solutions

1. Find the set of all integer values of x that satisfy the inequality: 3x - 5 < 7 and x ≥ 1.
   1. A) {2, 3}
   2. B) {1, 2, 3, 4}
   3. C) {0, 1, 2, 3}
   4. D) {1, 2, 3}
   Check my answer

   Correct answer: D) {1, 2, 3}

   3x - 5 < 7 → 3x < 12 → x < 4. Combined with x ≥ 1, the range is 1 ≤ x < 4. The integers in this interval are 1, 2, and 3.

   Show worked solution

   Step 1: Solve 3x - 5 < 7: add 5 to both sides → 3x < 12 → divide by 3 → x < 4. Step 2: Combine with given lower bound: 1 ≤ x < 4. Step 3: List integers in [1, 4): x ∈ {1, 2, 3}. Answer: {1, 2, 3}.
   Modelled on: the O/L Mathematics examination pattern
2. Solve the inequality 5 - 2x ≤ 11 and state the smallest integer value of x.
   1. A) x ≥ -8; smallest integer -8
   2. B) x ≤ -3; smallest integer -4
   3. C) x ≥ -3; smallest integer -3
   4. D) x ≥ 3; smallest integer 3
   Check my answer

   Correct answer: C) x ≥ -3; smallest integer -3

   Subtracting 5 gives -2x ≤ 6. Dividing by a negative number reverses the inequality sign, so x ≥ -3. The smallest integer that satisfies x ≥ -3 is -3 itself.

   Show worked solution

   Step 1: Subtract 5 from both sides: -2x ≤ 6. Step 2: Divide both sides by -2 and reverse the inequality sign: x ≥ -3. Step 3: The smallest integer satisfying x ≥ -3 is -3. Answer: x ≥ -3; smallest integer value -3.
   Modelled on: the O/L Mathematics examination pattern

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Where does Linear Inequalities fit in the syllabus?

Grade 10 · Term 3