Question

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

Answer 1

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

Explanation:

Bring the inequality to standard form -->
`f(x) = x^2 - 2x - 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 `-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.)