# How do you solve absolute value inequalities?

##### 1 Answer

Jul 22, 2018

There are many facets to this question. I will address a simply one and let the questioner expand to a specific example he/she may have.

Assume:

Then, either

Applying the rules of inequalities, either

Which leads to the compound inequality:

Therefore in solving absolute value inequalities of this and similar forms simply consider both positive and negative possibilities of the function and solve for each.

Example:

Either

Or

Thus:

Which can be expressed in interval notation as: