Answer
$(-2,3)$.
The graph is shown below.
Work Step by Step
The given compound inequality is
$3x+2\gt-4$ and $2x-1\lt5$.
Solve each inequality separately.
$\Rightarrow 3x+2\gt-4$ and $2x-1\lt5$.
$\Rightarrow 3x\gt-4-2$ and $2x\lt5+1$.
$\Rightarrow 3x\gt-6$ and $2x\lt6$.
$\Rightarrow x\gt-2$ and $x\lt3$.
First graph then take the intersection of the solution sets of the two inequalities.
The graph is shown in the image file.
We can write the compound inequality.
$x\gt-2$ as $(-2,\infty)$ and $x\lt3$ as $(-\infty,3)$
The intersection is
$(-\infty,3)\cap(-2,\infty)=(-2,3)$.
