Answer
The solution set is the region shaded GRAY
Work Step by Step
$-2 < y \leq 5$ means that
$\left\{\begin{array}{ll}
y > -2 & and\\
y \leq 5 &
\end{array}\right.$ , $\quad $simultaneously
We will graph the solution region for each inequality.
1. (red)
$y=-2 \quad $dashed line ( sign is $> )$,
... a horizontal line passing through ($0,-2$)
Testing (0,0):$\quad 0 >-2 \quad ?$
Yes, shade the region containing (0,0)
2 (blue)
$y=5 \quad $ solid line ( sign is $\leq )$,
... a horizontal line passing through ($0,5$)
Testing (0,0):$\quad 0 \leq 5 \quad ?$
Yes, shade the region containing (0,0)
The solution set is the region with BOTH shadings
The solution set is the region shaded GRAY