#### Answer

$(-\infty, -0.54) \cup (0.54, +\infty)$

#### Work Step by Step

Graph
$y_1 =\sqrt{0.5x^2+1}$ (the orange graph) and
$y_2=2|x|$ (the purple graph)
on the same coordinate plane.
(refer to the attached image below for the graph)
The solution to the given inequality is the set of x-values for which $y_1 \le y_2$.
Notice that $y_1$ (the orange graph) is less than or equal to $y_2$ in the following intervals:
$(-\infty, -0.54)$ and $(0.54, +\infty)$
Thus, the solution to the given inequality is:
$(-\infty, -0.54) \cup (0.54, +\infty)$