Answer
$(5.065, +\infty)$
Refer to the image below for the graph.
Work Step by Step
To solve the given inequality graphically, perform the following steps:
(1) Subtract $2$ on both sides of the inequality to obtain:
$x^3-4x^2-5x-2\gt 0$
Graph this inequality using a graphing utility.
(refer to the attached image in the answer part above for the graph)
(2) Identify the region/s where the graph is above the x-axis.
These are the regions where the value of $x^3-4x^2-5x-2$ is greater than $0$.
Note that the graph is above the x-axis in the interval $(5.065, +\infty)$.
Since the inequality involves $\gt$, then the endpoint $5.065$ is not part of the solution set.
Therefore, the solution set is:
$\color{blue}{(5.065, +\infty)}$
