Answer
$\left( -\dfrac{13}{2},0 \right)$
Work Step by Step
Using properties of equality, then,
\begin{array}{l}
-5\lt2(x+4)\lt8\\
-5\lt2x+8\lt8\\
-13\lt2x\lt0\\\\
-\dfrac{13}{2}\lt x\lt0
.\end{array}
In interval notation form, the solution is $
\left( -\dfrac{13}{2},0 \right)
$.