Intermediate Algebra (12th Edition)

$\left[ -10,0 \right]$
Using the properties of inequality, the given statement, $|x+5|-6\le-1 ,$ is equivalent to \begin{array}{l}\require{cancel} |x+5|\le-1+6 \\\\ |x+5|\le5 .\end{array} Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a$, then the inequality above is equivalent to \begin{array}{l}\require{cancel} -5\le x+5\le 5 .\end{array} Using properties of inequality, then \begin{array}{l}\require{cancel} -5\le x+5\le 5 \\\\ -5-5\le x+5-5\le 5-5 \\\\ -10\le x\le 0 .\end{array} Hence, the solution set is the interval $\left[ -10,0 \right] .$