Answer
$x=\{-23,23\}$
Work Step by Step
Using the properties of equality, the given equation, $
7+|x|=30
$, is equivalent to
\begin{array}{l}
7+|x|-7=30-7
\\\\
|x|=23
.\end{array}
Since $|x|=c$ implies $x=c$ or $x=-c$, then the solution to the equation, $
|x|=23
$, is
\begin{array}{l}\require{cancel}
x=23
\\\\\text{OR}\\\\
x=-23
.\end{array}
Hence, $
x=\{-23,23\}
$.
