Answer
$\left[ -10,0 \right]$
Work Step by Step
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]
.$
