Intermediate Algebra (12th Edition)

$x=\left\{ -19,9 \right\}$
Using the properties of equality, the given equation, $|x+5|-2=12 ,$ is equivalent to \begin{array}{l}\require{cancel} |x+5|=12+2 \\\\ |x+5|=14 .\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=14 \text{ OR } x+5=-14 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} x+5=14 \\\\ x=14-5 \\\\ x=9 \\\\\text{ OR } \\\\ x+5=-14 \\\\ x=-14-5 \\\\ x=-19 .\end{array} Hence, the solutions are $x=\left\{ -19,9 \right\} .$