#### Answer

$\left( -\infty, -4 \right]
\cup
\left[ 4,\infty \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|x|\ge4
,$ use the definition of absolute value inequalities.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ 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\ge4
\\\\\text{OR}\\\\
x\le-4
.\end{array}
In interval notation, the solution set is $
\left( -\infty, -4 \right]
\cup
\left[ 4,\infty \right)
.$
The colored graph is the graph of the solution set.