Answer
$(-2,-1)$.
The graph of the solution set is shown below.
Work Step by Step
The given compound inequality is
$2x+4\lt2$ and $x-3\gt-5$.
Solve each inequality separately.
First $=2x+4\lt2$
Subtract $4$ from both sides.
$=2x+4-4\lt2-4$
Simplify.
$=2x\lt-2$
Divide both sides by $2$.
$=\frac{2x}{2}\lt\frac{-2}{2}$
Simplify.
$=x\lt-1$
Second $x-3\gt-5$
Add $3$ to both sides.
Second $x-3+3\gt-5+3$
Simplify.
Second $x\gt-2$
First graph and then take the intersection of the two inequality.
We can write the compound inequality.
$x\lt-1$ as $(-\infty,-1)$ and $x\gt-2$ as $(-2,\infty)$
The intersection is
$(-\infty,-1)\cap(-2,\infty)=(-2,-1)$.
The combined graph is shown in the image file.
