Absolute Value Equations and Inequalities

Which college will you attend? Who knows. Will that cutie in your history class ask you to prom? No clue. Will it rain the night of homecoming? Hopefully not, but it could. Will you beat every level in Peggle? Possibly, but probably not.

The point is that few things in life are absolute—except absolute values, that is.

The absolute value of any number is how far away the number is from 0. If you walk 5 blocks west from your house, you will be 5 blocks away from your house. If you walk 5 blocks east from your house, you will again be 5 blocks away from your house.

This sort of thinking can also be applied to the absolute values of real numbers. The number 5 is 5 units away from 0. Similarly, -5, which is on the opposite side of 0 on a number line, is also 5 units away from 0.

To show that we're looking for an absolute value, we put two little bars on the outside of the number or expression, like this: |5| or |-5|. Those bars make everything inside turn positive, so |5| and |-5| both have the exact same value.

|5| = 5

|-5| = 5

Absolute value. Is it cool? Absolutely. You probably saw that one coming from |±20 miles| away.