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CA Foundation · Quantitative Aptitude · Linear Inequalities

The solution set of 2x − 3 ≥ 5 together with 3x + 1 < 22, where x is a real number, is:

The solution set is [4, 7). The first inequality gives x ≥ 4 and the second gives x < 7. Their intersection includes 4 because the first sign is ≥, and excludes 7 because the second is strict.

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

Explanation

2x − 3 ≥ 5 gives x ≥ 4. 3x + 1 < 22 gives 3x < 21, so x < 7. The common solution is 4 ≤ x < 7, i.e. [4, 7). Option (4, 7] reverses which end is included.

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