Answer
$6\geq z\geq -2$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 19\geq 3z+1 \geq -5$
Subtract $1$ from each expression.
$\Rightarrow 19-1\geq 3z+1-1 \geq -5-1$
Simplify.
$\Rightarrow 18\geq 3z \geq -6$
Divide each side by $3$.
$\Rightarrow \frac{18}{3}\geq \frac{3z}{3} \geq \frac{-6}{3}$
Simplify.
$\Rightarrow 6\geq z\geq -2$
Hence, the solution is $6\geq z\geq -2$.
