Answer
$-7\le x \le 7$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
3\ge \dfrac{x-1}{2} \ge -4
.$ 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}
3\ge \dfrac{x-1}{2} \ge -4
\\\\
2(3)\ge 2\left( \dfrac{x-1}{2} \right) \ge 2(-4)
\\\\
6\ge x-1 \ge -8
\\\\
6+1\ge x-1+1 \ge -8+1
\\\\
7\ge x \ge -7
\\\\
-7\le x \le 7
.\end{array}
The graph includes the points from $-7$ (inclusive) to $7$ (inclusive).
