#### Answer

$x\gt7
\\\\\text{OR}\\\\
x\lt-7$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|x|\gt7
,$ use the definition of absolute value inequality. Then graph the solution set.
In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|\gt c$ implies $x\gt c \text{ or } x\lt-c$ (which is equivalent to $|x|\ge c$ implies $x\ge c \text{ or } x\le-c$), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
x\gt7
\\\\\text{OR}\\\\
x\lt-7
.\end{array}
The graph above confirms the solution set of the inequality.