# How do you solve the inequality: #9x - x^2<=20#?

##### 2 Answers

#### Explanation:

is equivalent to

or, after factoring,

if both terms are

or if both terms are

Solve

Ans: (-infinity, 4] and [5, infinity)

#### Explanation:

Standard form: f(x) = - x^2 + 9x - 20 <= 0

First solve the quadratic equation y = - x^2 + 9x - 20 = 0. Factor pairs of ac = 20 -> (2, 10)(4, 5). This sum is 9 = b (a < 0)

The 2 real roots are: 4 and 5.

Since a < 0. the parabola opens downward, between the 2 real roots 4 and 5, f(x) > 0, and f(x) < 0 outside this interval.

The 2 critical points 4 and 5 are included in the solution set.

Answer by half closed intervals: (-infinity, 4] and [5, +infinity)

graph{-x^2 + 9x - 20 [-10, 10, -5, 5]}