Answer
$[0,4]\cup[6,\infty)$
Work Step by Step
Step 1. Rewrite the inequality as
$x(x-4)(x-6)\geq0$
The boundary points are $x=0,4,6$
Step 2. Using the test points to examine signs across the boundary points, we have
$...(-)...(0)...(+)...(4)...(-)...(6)...(+)...$
Thus, the solutions are:
$0\leq x\leq 4$ plus $x\geq6$
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 $[0,4]\cup[6,\infty)$
