Answer
$[0,1]$
Work Step by Step
Step 1. Rewrite the inequality as
$-x(x-1)\geq0$ or $x(x-1)\leq0$
and the boundary points are $x=0,1$
Step 2. Using the test points to examine signs across the boundary points, we have
$...(+)...(0)...(-)...(1)...(+)...$
Thus the solutions are $0\leq x\leq 1$
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 $[0,1]$
