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