Answer
The solution is all real numbers.
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow x-8\leq 4$ or $2x+3 \gt 9$
Solve the first inequality.
$\Rightarrow x-8\leq 4$
Add $8$ to each side.
$\Rightarrow x-8+8\leq 4+8$
Simplify.
$\Rightarrow x\leq 12$
Solve the second inequality.
$\Rightarrow 2x+3 \gt 9$
Subtract $3$ from each side.
$\Rightarrow 2x+3-3 \gt 9-3$
Simplify.
$\Rightarrow 2x\gt 6$
Divide each side by $2$.
$\Rightarrow \frac{2x}{2}\gt \frac{6}{2}$
Simplify.
$\Rightarrow x\gt 3$
Merge the overlap solution
Hence, the solution is all real numbers.
