#### Answer

$-7\lt x\lt7$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|x|\lt7
,$ use the definition of absolute value inequality. Then graph the solution.
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 $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-7\lt x\lt7
.\end{array}
The graph above confirms the solution set of the inequality.