#### Answer

$-5\le x \le 7$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
-18\le 4x+2\le30
.$ Then graph.
In the graph above, a hollowed dot is used for $\lt$ or $\gt$. A shaded dot is used for $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
-18\le 4x+2\le30
\\\\
-18-2\le 4x+2-2\le30-2
\\\\
-20\le 4x\le28
\\\\
-\dfrac{20}{4}\le \dfrac{4x}{4}\le\dfrac{28}{4}
\\\\
-5\le x \le 7
.\end{array}
The graph includes the points from $-5$ (inclusive) to $7$ (inclusive).