Answer
$(-\infty,-3)$
Work Step by Step
Step 1. Factor the inequality as
$x^2(x-3)-9(x-3)\lt0$
or
$(x-3)^2(x+3)\lt0$
The the boundary points are $x=-3,3$
Step 2. Using test points to examine signs across the boundary points, we have
$...(-)...(-3)...(+)...(3)...(+)...$
Thus, the solutions are:
$x\lt-3$
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 $(-\infty,-3)$
