Answer
$[0,4]$
Work Step by Step
We are given that $x^{2}-4x\leq0$. To solve, we can first solve the related equation, $x^{2}-4x=0$.
$x^{2}-4x=0$
Factor an x out of both terms on the left side.
$x(x-4)=0$
Therefore, $x=0$ or $x=4$.
We can now test numbers around these values by plugging them into the equation.
$(-1)^{2}-4(-1)=1+4=5\gt0$
$(1)^{2}-4(1)=1-4=-3\lt0$
$(5)^{2}-4(5)=25-20=5\gt5$
Therefore, we know that values of x between and including 0 and 4 satisfy the given inequality.
