A is true because absolute value is never negative, so |x| ≥ 0 for all real x. B is true: |x| 0) means x lies within distance a of 0, i.e., −a < x a means x is outside that interval, i.e., x a. D is false because |x| > −2 is true for every real x (since |x| ≥ 0), so it does not force x to be positive. Therefore A, B and C only are correct.
Option A:
Option A is incorrect because it omits C, even though the standard “outside interval” solution for |x| > a is a key absolute-value inequality fact.
Option B:
Option B is correct because it contains all and only the true statements (A, B, C) and excludes D, which is a false restriction about positivity.
Option C:
Option C is incorrect because it includes D, which is not a valid implication from |x| > −2, so this option contains a false statement.
Option D:
Option D is incorrect because it omits A (a fundamental fact: |x| is always ≥ 0) and includes D (false), so it cannot be correct.
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