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

##### 2 Answers

#### Answer:

#### 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

#### Answer:

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