  # Algebra Absolute Value

Curious what this algebra absolute value stuff is all about?

 This page is used to explain the definition and the basics of absolute value. If you want to know how to solve an absolute value equation, then please visit GradeA's absolute value equation page. In the sections below, you will learn about the definition of an absolute value, and then you will learn how to evaluate them (it is really easy!).

 The Definition of Absolute Value: The Distance from 0

The formal definition of the absolute value of a number goes as follows:

The absolute value of a number is the distance that number is from zero on a number line.

Take a look at the pictorial representation below. If you need it, get more information about the number line.

To find|5| (known as "the absolute value of 5") find the distance that 5 is from 0. Because 5 is 5 units from 0, that means that|5| = 5.

Let's look at another example. Now lets find |-4| . Because -4 is 4 unit from 0, that means that |-4| = 4.

 Evaluating Absolute Values: Find the Pattern

Using the two examples above, can you find the pattern for evaluating algebra absolute values? Positive Numbers: Notice that for every positive number, the distance the number is from 0 is the same as the number.

|Positive Number| = Positive Number

Negative Numbers: Notice now that the number is the same, but the negative sign is dropped. You know that a distance cannot be negative (you can't be negative 6 feet tall!). Because absolute value is the distance from zero, it also cannot be negative!

|Negative Number| = Number without the Negative Sign

 Absolute Value Equations, Inequalities, and More

There's a lot more to an algebra absolute value than just the definition.

 You will also need to know how to solve absolute value equations - equations involving absolute values. An even more advanced topic is absolute value inequalities - these are more difficult to solve, but don't worry, with GradeA you will have no trouble at all!