# How do you solve the inequality #x^2 - 9x> -18#?

##### 2 Answers

The solutions are

#### Explanation:

The inequality is

Let

Let's build a sign chart

Therefore,

graph{x^2-9x+18 [-4.29, 15.71, -3.96, 6.04]}

(-inf., 3) and (6, +inf.)

#### Explanation:

Find 2 real roots, that have same sign(ac > 0), knowing the sum (- b = 9) and the product (c = 18). They are 6 and 3.

The graph of f(x) is an upward parabola (a > 0).

Inside the interval (3, 6) --> f(x) < 0 as the graph is below the x-axis.

Outside the interval (3, 6) --> f (x )> 0. Therefor, the solution set is the 2 open intervals:

(- inf., 3) and (6, +inf.)