Answer
$\left\{x| -15.5\le x \le 16.5\right\}$
Work Step by Step
Multiply $-4$ to each part.
Note that when a negative number is multiplied to an inequality, the inequality symbols change to their opposite direction.
\begin{align*}
\require{cancel}
-4(-9)\ge -4\left(\frac{2x+3}{-4}\right)&\ge -4(7)\\
36\ge 2x+3&\ge -28\\
\end{align*}
Subtract $3$ from each part:
$$33\ge 2x \ge -31$$
Divide each part by $2$ to obtain:
\begin{align*}
&16.5 \ge x \ge -15.5&\\\\
&-15.5 \le x \le 16.5\end{align*}
The solution set is $\left\{x|-15.5\le x \le 16.5\right\}$.
To graph the solution set, plot solid dots at $-15.5$ and $1.5$, then shade the region in between.
Refer to the graph above.
