Answer
$-3\le x \le 1$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given, $
1\le 3-2x \le 9
.$ Then graph the solution set.
In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
1\le 3-2x \le 9
\\\\
1-3\le 3-2x-3 \le 9-3
\\\\
-2\le -2x \le 6
.\end{array}
Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-2\le -2x \le 6
\\\\
\dfrac{-2}{-2}\le \dfrac{-2x}{-2} \le \dfrac{6}{-2}
\\\\
1\ge x \ge -3
\\\\
-3\le x \le 1
.\end{array}
