# How do you solve and write the following in interval notation:  -3x <= -x^2 ?

Jul 13, 2016

$x \in \left[0 , 3\right]$

#### Explanation:

If $\left(x - a\right) \left(x - b\right) < 0$, then $x \in \left(a , b\right) .$. In other words, x is in between a

and b.

Here, ,

$x \left(x - 3\right) \le 0$.

So, x and (x-3) should have opposite signs for $x \left(x - 3\right) < 0$

And so, $x \in \left[0 , 3\right]$.