Question

Solve the following inequality for x. x-9<2(9-x)

Answer 1

Answer:

Step-by-step 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]}

Answer 2

Answer: x<9 (x is less than or equal to 9)