Question

How do you solve the inequality `x>x^2` and write your answer in interval notation?

Answer 1

`x < 0 and > 1`

Explanation:

`x=x^2=x(1-x)>0`.

So, x and (1-x) have the same sign.

When `x > 1`, both are positive.

When `x < 0`, both are negative,

When `x in (0, 1)`, they have opposite signs.