Answer
$(1,\infty)$
Work Step by Step
Step 1. Factor the inequality as
$x^2(x-1)+9(x-1)\gt0$
or
$(x-1)(x^2+9)\gt0$
Then the boundary point is $x=1$
Step 2. Using test points to examine signs across the boundary points, we have
$ ...(-)...(1)...(+)...$
Thus the solutions are $x\gt1$
Step 3. We can express the solutions on a real number line as shown in the figure.
Step 4. We can express the solutions in interval notation as $(1,\infty)$
