How do you solve the inequality #abs(x-3)-abs(2x+1)<0# and write your answer in interval notation?
Assuming x is real, use the alternate form:
This implies that:
Expand the squares and solve the resulting quadratic inequality.
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:
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