Answer
$x=14 \text{ OR } x=-14$
Work Step by Step
Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the solutions to the given equation, $
|x|=14
,$ are
\begin{array}{l}\require{cancel}
x=14 \text{ OR } x=-14
.\end{array}
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