# How do you solve and write the following in interval notation: x^2-8x>0?

Jun 24, 2016

Solution is either $x < 0$ or $x > 8$.
We can also write this as $| x - 4 | > 4$

#### Explanation:

As ${x}^{2} - 8 x > 0$ i.e. $x \left(x - 8\right) > 0$

either $x > 0$ and $x - 8 > 0$ (i.e. $x > 8$)
and these both conditions would be satisfied if $x > 8$

or $x < 0$ and $x - 8 < 0$ (i.e. $x < 8$)
and these both conditions would be satisfied if $x < 0$

Hence, solution is either $x < 0$ or $x > 8$.

We can also write this as $| x - 4 | > 4$