# How do you solve #(x(x-4))/(2-3x)<= 3#?

##### 2 Answers

#### Explanation:

Multiplying the numerator by x gives

Multiplying by the denominator gives

Rearranging gives

Factoring gives

For the inequality to be true one term must be positive and the other negative

This means

This means

Or

Compare to

#### Explanation:

Rewrite to get a single ratio on the left.

Find the key numbers (partition numbers, unnamed special numbers) for the expression on the left. These are the places where the expression **might** change sign. We find them by finding the zeros and the places where the expression is undefined.

In the end we solve

The key numbers are:

They cut the real number line into intervals:

The expression:

positive on

negative on

positive on

negative on

We want the value of