Answer
$(-1.855, -0.597) \cup (0.452, 2)$
Refer to the image below for the graph.
Work Step by Step
To solve the given inequality graphically, perform the following steps:
(1) Let each side of the equation represent a function then graph each function on the same coordinate plane.
Graph $y=x^4-4x^2$ (the blue graph) and $y=\dfrac{1}{2}x-1$ (the red graph).
(refer to the attached image in the answer part above for the graph)
(2) Identify the region/s where the blue graph has a smaller value than the red graph. The interval/s that cover these regions make up the solution set of the given inequality.
Note that the blue graph is lower than the red graph in the following intervals:
$(-1.855, -0.597)$ and $(0.452, 2)$
This means that the value of $x^4-4x^2$ is less than the value of $\dfrac{1}{2}x-1$ in the intervals $(-1.855, -0.597)$ and $(0.452, 2)$
Since the inequality involves $\lt$, then the endpoints $-1.855, -0.597, 0.452,$ and $2$ are not part of the solution set.
Therefore, the solution set is:
$(-1.855, -0.597) \cup (0.452, 2)$
