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CA Foundation · Quantitative Aptitude · Linear Inequalities

The solution set of the system x + 2 > 5 and 2x − 3 ≤ 11, where x is a real number, is:

The solution is (3, 7]. The first inequality gives x > 3 and the second gives x ≤ 7. Since both must hold together, x lies strictly above 3 and up to and including 7.

  1. A(3, 7]Correct
  2. B[3, 7)
  3. C(−∞, 3) ∪ [7, ∞)
  4. D(3, 7)

Explanation

x + 2 > 5 gives x > 3. 2x − 3 ≤ 11 gives 2x ≤ 14, so x ≤ 7. Both must hold, so 3 < x ≤ 7, which is (3, 7]. Option [3, 7) wrongly swaps the end-point inclusion.

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