Answer
$-3\le a\le3$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Solve the given inequality, $
|a|\le3
,$ using the definition of a less than absolute value inequality. 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 $\ge.$
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), the given inequality is equivalent to
\begin{array}{l}\require{cancel}
-3\le a\le3
.\end{array}
The graph consists of all points from $-3$ (inclusive) up to $3$ (inclusive).
