#### Answer

$\color{blue}{[-9, 9]}$

#### Work Step by Step

Multiply $2$ to each part:
\begin{array}{ccccc}
&2(-4)&\le &2 \cdot \dfrac{x+1}{2} &\le &2(5)
\\&-8 &\le &x+1 &\le &10
\end{array}
Subtract $1$ to each part:
\begin{array}{ccccc}
\\&-8-1 &\le &x+1-1 &\le &10-1
\\&-9 &\le &x &\le &9
\end{array}
Thus, the solution to the given inequality is:
$\color{blue}{[-9, 9]}$