Question

solve the absolute value inequality.
|x| > 14
select the correct choice below and, if necessary, fill in the answer box to compl
a. the solution set in interval notation is
(simplify your answer.)
b. the solution set is ∅.

Explanation:

Step1: Recall absolute value inequality rule

For \(|x| > a\) (where \(a>0\)), the solution is \(x < -a\) or \(x > a\). Here, \(a = 14\), so we get two inequalities: \(x < - 14\) or \(x > 14\).

Step2: Write in interval notation

The interval for \(x < - 14\) is \((-\infty, - 14)\) and for \(x > 14\) is \((14, \infty)\). Combining these, the solution set in interval notation is \((-\infty, - 14)\cup(14, \infty)\).

Answer:

\((-\infty, - 14)\cup(14, \infty)\)