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CA Foundation · Quantitative Aptitude · Linear Inequalities

The solution of the double inequality −7 < 3 − 2x ≤ 9, where x is real, is:

The solution is −3 ≤ x < 5. Subtracting 3 gives −10 < −2x ≤ 6, and dividing by −2 reverses the signs, giving 5 > x ≥ −3. The strict end stays at 5 and the included end at −3.

  1. A−3 ≤ x < 5Correct
  2. B−3 < x ≤ 5
  3. C−5 < x ≤ 3
  4. D−5 ≤ x < 3

Explanation

Subtract 3 throughout: −10 < −2x ≤ 6. Divide by −2, which reverses the signs: 5 > x ≥ −3, that is −3 ≤ x < 5. Check: x = −3 gives 9 (allowed, equal to the upper limit) and x = 5 gives −7 (not allowed since strict). Option B wrongly keeps the original end-point types.

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