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CA Foundation · Quantitative Aptitude · Linear Inequalities

Solve for real x: (x − 3)/4 − (2x + 1)/6 ≤ 1.

The solution is x ≥ −23, because dividing by −1 reverses the inequality sign.

  1. Ax ≥ −17Correct
  2. Bx ≤ −17
  3. Cx ≥ 17
  4. Dx ≤ 17

Explanation

Multiply both sides by 12, which is positive: 3(x − 3) − 2(2x + 1) ≤ 12. This gives 3x − 9 − 4x − 2 ≤ 12, so −x − 11 ≤ 12 and −x ≤ 23. Multiplying by −1 reverses the sign, so x ≥ −23. Check x = 0: −3/4 − 1/6 = −11/12, which is ≤ 1. Check x = −30: −33/4 + 59/6 = 19/12, which is greater than 1, so it is rejected. Hence the answer is x ≥ −23, which is not among the options.

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