## College Algebra (11th Edition)

$x=\{ -11,3 \}$
Since for any $a\gt0$, $|x|=a$ implies $x=a$ or $x=-a$, then the given inequality, $|x+4|=7 ,$ is equivalent to \begin{array}{l}\require{cancel} x+4=7 \\\text{ OR }\\ x+4=-7 .\end{array} Solving each equation separately, then, \begin{array}{l}\require{cancel} x=7-4 \\\\ x=3 \\\text{ OR }\\ x+4=-7 \\\\ x=-7-4 \\\\ x=-11 .\end{array} Hence, $x=\{ -11,3 \} .$