Absolute Value and Additive Inverse

Additive Inverse and Absolute value are similar concepts, but it is important to understand

their differences. Also, you need to be able to define them using numeric examples as well

as in algebraic terms.

Definition of Additive Inverse

• The Additive Inverse of a number is its mirror image on the number line. The additive inverse of -5 is 5 and the additive inverse of 5 is -5.

• If a number is positive, its additive inverse is negative and if a number is negative, its additive inverse is positive

• Additive inverse can also be defined as what you add to a number to get 0, i.e. 5 + (-5) = 0.

… -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 …

Definition of Absolute Value

• The Absolute Value of a number is always a positive number. The absolute value of x is written |x|.

• |5| = 5 and |-5| = 5• Absolute value can be described as the distance from

0 on a number line. 5 and -5 are both 5 units away from 0 on the number line.

… -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 …

Algebraic Descriptions

Let’s look at the algebraic description of these terms. Make sure you understand them as well.

•The additive inverse of x is –x

•If x ≥ 0 , then |x| = x

•If x < 0, then |x| = -x

If x were = 5, then its additive inverse would be -5 and if x were equal to -5, its additive inverse would be –(-5) or simply written as 5.

This means x is either 0 or a positive number, and since absolute values are positive, we know the absolute value is the number itself.

If x is a negative number, such as -5, then its absolute value is its additive inverse –(-5) or 5, because it always has to be a positive number.