# How do you solve the inequality x^2 - x - 3 > x?

Apr 17, 2016

(-inf., -1) and (3, inf.)

#### Explanation:

Bring the inequality to standard form -->
$f \left(x\right) = {x}^{2} - 2 x - 3 > 0$
First, Find the 2 real roots (or x-intercepts):
Since a - b + c = 0, use shortcut. The 2 x-intercepts are: -1
and $- \frac{c}{a} = 3.$
Since a > 0, the parabola graph opens upward. Between the 2 x-intercepts, f(x) < 0. Outside the 2 x-intercepts, f(x) > 0.
Answer by open interval: (-inf., -1) and (3, inf.)