Answer
$\left[ -2, -\dfrac{9}{5} \right)$
Work Step by Step
Using compound inequalities, the solution to the given inequality, $
-2\le8+5x\lt-1
,$ is
\begin{array}{l}\require{cancel}
-2-8\le8+5x-8\lt-1-8
\\\\
-10\le 5x\lt-9
\\\\
-\dfrac{10}{5}\le \dfrac{5}{5}x\lt-\dfrac{9}{5}
\\\\
-2\le x\lt-\dfrac{9}{5}
.\end{array}
In interval notation, the solution is $
\left[ -2, -\dfrac{9}{5} \right)
.$