Question

can somebody tell me how to solve this inequality equation?

(a-2)(a-3)<0

I know the opposite was 2 and 3..but how do i determine the greater than, less than or equal to? Explain please.

Answer 1

Eq1. Given: (x - 2) (x - 3) < 0.

Eq2. Graph (x - 2) (x - 3) = 0,
x - 2 = 0,
x = 2 = x-Int.

x - 3 = 0,
x = 3 = x-Int.

Find the coordinates of the vertex:
h = Ave of the x-Ints,
h = Xv = (2 + 3) / 2 = 2.5.

Substitute 2.5 for x in Eq2 to get
y coordinate of vertex:

k = Yv = (2.5 - 2) (2.5 - 3) = -0.25.

V(h , k) = V(2.5 , -0.25).

Use the coordinates of the vertex and x-ints to sketch the graph:

(2 , 0) , V(2.5 , -0.25) , (3 , 0).

Your inequality uses the < sign.
So all points on the graph between the
X-Ints are negative(less than 0) and
satisfy the inequality.

In Eq form: 2 < X < 3.
The Eq states that all values of x >
2 but < 3 satisfy the inequality.

Answer 2

You can use the letter a as your variable if you desire. I didn't mean to use x.