# For what #x# is #3/(x+3)>(4x)/(x-2)#?

##### 1 Answer

#### Explanation:

To simplify the inequality, we are going to perform cross-multiplication of the denominator to avoid dealing with fractions. However, the sign of the inequality might be flipped if we multiply both sides by a negative expression. Hence, we consider

For the case of

The sign remains the same as the product of 2 negative expressions is positive.

Completing the square,

Since the RHS is always

Therefore, no value of

For the case of

The sign flips as the product of a positive and a negative expressions is negative.

Completing the square,

Since the RHS is always

Therefore, all values of

For the case of

The sign remains the same as the product of 2 negative expressions is positive.

Completing the square,

Since the RHS is always

Therefore, no value of

Combining the solutions on all 3 intervals, we get

if and only if