Answer
$c\leq-2 $ or $c\gt 7$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 4c+3\leq -5$ or $c-8 \gt -1$
Solve the first inequality.
$\Rightarrow 4c+3\leq -5$
Subtract $3$ from each side.
$\Rightarrow 4c+3-3\leq -5-3$
Simplify.
$\Rightarrow 4c\leq -8$
Divide each side by $4$.
$\Rightarrow \frac{4c}{4}\leq \frac{-8}{4}$
Simplify.
$\Rightarrow c\leq -2$
Solve the second inequality.
$\Rightarrow c-8\gt -1$
Add $8$ to each side.
$\Rightarrow c-8+8\gt -1+8$
Simplify.
$\Rightarrow c\gt 7$
Hence, the solution is $c\leq-2 $ or $c\gt 7$.
