Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x=\{-23,23\}$
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, $x=\{-23,23\}$.