Answer
$x\lt-6.5
\text{ OR }
x\gt6.5$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|x|\gt6.5
,$ use the definition of 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}
x\gt6.5
\\\\\text{OR}\\\\
x\lt-6.5
.\end{array}
Hence, the solution set is $
x\lt-6.5
\text{ OR }
x\gt6.5
.$
