# How do you solve the inequality #abs(x-3)-abs(2x+1)<0# and write your answer in interval notation?

##### 1 Answer

Sep 13, 2017

Assuming x is real, use the alternate form:

This implies that:

Expand the squares and solve the resulting quadratic inequality.

#### Explanation:

Starting with the above:

Expand the squares

Combine like terms:

The quadratic will be greater than 0 to the left and to the right of the roots, therefore, we should find the roots:

Factor:

The intervals to the left and to the right of these roots are:

Here is a graph of

Please observe that it drops below the