Answer
$(-\infty,-4]\cup[\frac{1}{2},\infty)$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow 9\leq \left | 4x+7\right |$
Switch sides.
$\Rightarrow \left | 4x+7\right | \geq 9$
Rewrite the inequality without absolute value bars.
$\Rightarrow 4x+7\leq-9$ or $4x+7\geq9$
Solve each inequality separately.
Subtract $7$ from all parts.
$\Rightarrow 4x+7-7\leq-9-7$ or $4x+7-7\geq9-7$
Simplify.
$\Rightarrow 4x\leq-16$ or $4x\geq2$
Divide all parts by $4$.
$\Rightarrow \frac{4x}{4}\leq\frac{-16}{4}$ or $\frac{4x}{4}\geq\frac{2}{4}$
Simplify.
$\Rightarrow x\leq-4$ or $x\geq\frac{1}{2}$
The solution set is les than or equal to $-1$ or greater than or equal to $2$.
The interval notation is
$(-\infty,-4]\cup[\frac{1}{2},\infty)$.
