## Intermediate Algebra (6th Edition)

$[0,4]$
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.