## Intermediate Algebra (12th Edition)

$x=\left\{ -5,5 \right\}$
Using the properties of equality, the given equation, $|x|-1=4 ,$ is equivalent to \begin{array}{l}\require{cancel} |x|=4+1 \\\\ |x|=5 .\end{array} Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the equation above is equivalent to \begin{array}{l}\require{cancel} x=5 \text{ OR }x=-5 .\end{array} Hence, the solutions are $x=\left\{ -5,5 \right\} .$