Answer
$a\lt-5 \text{ or } a\gt5$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|a|\gt5
,$ use the definition of a greater than (greater than or equal to) 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 $c\gt0$, $|x|\gt c$ implies $x\gt c \text{ or } x\lt-c$ (which is equivalent to $|x|\ge c$ implies $x\ge c \text{ or } x\le-c$), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
a\gt5
\\\\\text{OR}\\\\
a\lt-5
.\end{array}
Hence, the solution set is $
a\lt-5 \text{ or } a\gt5
.$
