Absolute value, represented as a vertical line on either side of the value, refers to a number or variable’s distance from zero on the number line. There are always two numbers that share the same distance from zero: a positive number and its negative counterpart.
Thus, the absolute value of a number is that number without a positive or negative sign. For example:
|4| = 4
|-4| = 4
Both of these values (4 and -4) are equidistant from 0, and thus have the same absolute value.
If you are ever confused by absolute value, just remember that absolute value is capturing the distance of a number from 0. Here are a few more examples.
It’s also important to understand how to solve a problem with absolute value, or to solve for a variable (x) in an equation with absolute value. Take a look at the following three examples:
Some absolute value problems can be quite tricky, but you can solve all absolute value questions by making sure to account for the both the positive and negative counterparts.
Answers to Practice Problems