In many real-world situations, it is okay if an item is not exactly the perfect length or weight. There is a range of values that will work: The length or weight of the item can be within a certain amount or at least a certain amount away. In these cases, it can be useful to write the range of values that work as inequalities that include absolute values.

To be within a certain distance of a value, we can write an inequality of the form . The solutions to this inequality can be drawn on a number line like this:

To be at least a certain distance away from a value, we can write an inequality of the form . The solutions to this inequality can be drawn on a number line like this:

For example, to fence in a circular area with a radius of 100 meters, we should use the equation and buy meters of fencing. This is difficult to do because is an irrational number. Maybe it’s okay if we don’t make a perfect circle or if it’s a little off, so if we buy amount of fence, where is a solution to , we will have the right amount of fencing within 1 meter of the exact value, and that should be close enough.