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CA Foundation · Quantitative Aptitude · Linear Inequalities

The solution of the system 3x − 5 ≥ 4 and 7 − x > 2, for real x, is:

The first inequality gives x at least 3 and the second gives x less than 5. Since both must hold together, the solution is the intersection, 3 ≤ x < 5, with 3 included and 5 excluded.

  1. A3 ≤ x < 5Correct
  2. Bx ≥ 3 or x < 5
  3. C3 < x ≤ 5
  4. Dx ≥ 3

Explanation

3x − 5 ≥ 4 gives 3x ≥ 9, so x ≥ 3. 7 − x > 2 gives x < 5. Both must hold, so 3 ≤ x < 5. Option with 'or' wrongly takes the union.

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