Answer
$(-\infty, -0.599] \cup [-2.449, 2.449] \cup [5.099, +\infty)$
Work Step by Step
To solve the given inequality graphically, do the following steps:
(1) Use a graphing utility to graph $y=|x^2-16|-10$ (refer to the red graph) and $y=0$ (refer to the blue graph);
(2) Identify the points where the graphs intersect each other.
The graphs intersect at:
$x\approx -5.099$
$x \approx -2.449$
$x \approx 2.449$
$x \approx 5.099$
(3) Identify which region/s satisfy the given inequality.
Notice that the $y=|x^2-16|-10$ (the red graph) is above (above means greater in value) $y=0$ (the blue graph) in the following intervals:
$(-\infty, -0.599]$
$[-2.449, 2.449]$
$[5.099, +\infty)$
The inequality involves less than so all the boundary numbers are not included in the solution.
Thus, the solution to the given inequality is:
$(-\infty, -0.599] \cup [-2.449, 2.449] \cup [5.099, +\infty)$
(refer to the attached image below for the graph)
