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CA Foundation · Quantitative Aptitude · Linear Inequalities

The set of all real values of x satisfying |2x − 5| ≤ 7 is:

The solution is −1 ≤ x ≤ 6. An absolute value being at most 7 means the expression lies between −7 and 7. Adding 5 and halving yields the interval from −1 to 6. The 'or' form would apply only to the 'at least 7' case.

  1. A−1 ≤ x ≤ 6Correct
  2. B1 ≤ x ≤ 6
  3. Cx ≤ −1 or x ≥ 6
  4. D−6 ≤ x ≤ 1

Explanation

|2x − 5| ≤ 7 means −7 ≤ 2x − 5 ≤ 7. Adding 5 gives −2 ≤ 2x ≤ 12, and dividing by 2 gives −1 ≤ x ≤ 6. The option with 'or' describes |2x − 5| ≥ 7, which is the opposite inequality.

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