Question

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

Answer 1

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

Explanation:

As `x^2-8x>0` i.e. `x(x-8)>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`