The solution set of the inequality |x| ≤ a is - a ≤ x ≤ a. (Correct choice: D)
How to solve an inequality using an absolute value
In accordance with algebra, the absolute value is an algebraic form defined by two cases:
- |x| = x for x ≥ 0.
- |x| = - x for x < 0.
Then, the inequality |x| ≤ a is equivalent to - x ≤ a for x < 0 and x ≤ a for x ≥ 0, and whose solution set is:
x ≥ - a and x ≤ a, that is, - a ≤ x ≤ a.
The solution set of the inequality |x| ≤ a is - a ≤ x ≤ a. (Correct choice: D)
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