Answer
$\color{blue}{(-\infty, -5.099] \cup [-2.499, 2.499] \cup [5.099, +\infty)}$
Refer to the image below for the graph.
Work Step by Step
To solve the given inequality graphically, perform the following steps:
(1) Let the left side the inequality represent a function then graph using a graphing utility.
Graph $y=|x^2-16|=10$.
(refer to the attached image in the answer part above for the graph)
(2) Identify the region/s where graph is above the x-axis.
Note that the graph is above the x-axis in the following intervals:
$(-\infty, -5.099)$, $(-2.499, 2.499)$, and $(5.099, +\infty)$
This means that the value of $|x^2-16|-10$ is greater than or equal to 0 in the intervals $(-\infty, -5.099)$, $(-2.499, 2.499)$, and $(5.099, +\infty)$.
Since the inequality involves $\ge$, then the endpoints $-5.099, -2.499, 2.499,$ and $5.099$ are part of the solution set.
Therefore, the solution set is:
$\color{blue}{(-\infty, -5.099] \cup [-2.499, 2.499] \cup [5.099, +\infty)}$
