Answer
$(-1.927, -0.597) \cup (0.452, 2)$
Work Step by Step
To solve the given inequality graphically, do the following steps:
(1) Use a graphing utility to graph $y=x^4$-4x^2 (refer to the red graph) and $y=\frac{1}{2}x-1$ (refer to the blue graph);
(2) Identify the points where the graphs intersect each other.
The graphs intersect at:
$x\approx -1.927$
$x \approx -0.597$
$x \approx 0.452$
$x =2$
(3) Identify which region/s satisfy the given inequality.
Notice that from $x=-1.927$ to $x=-0.597$, and from $x=0.452$ to $x=2$, the graph of $y=x^4-4x^2$ (the red graph) is below the graph $y=\frac{1}{2}x-1$ (the blue graph). Below means that the value of the function is less than the other.
The inequality involves less than so all the boundary numbers are not included in the solution.
Thus, the solution to the given inequality is:
$(-1.927, -0.597) \cup (0.452, 2)$
(refer to the attached image below for the graph)
