Answer
The solution is $y\gt 7$.
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow -y+3\leq 8$ and $y+2\gt 9$
Solve the first inequality.
$\Rightarrow -y+3\leq 8$
Add $y-8$ to each side.
$\Rightarrow -y+3+y-8\leq 8+y-8$
Simplify.
$\Rightarrow -5\leq y$
Solve the second inequality.
$\Rightarrow y+2\gt 9$
Subtract $2$ from each side.
$\Rightarrow y+2-2\gt 9-2$
Simplify.
$\Rightarrow y\gt 7$
Overlap the solutions.
$\Rightarrow y\gt 7$
Hence, the solution is $y\gt 7$.
