Definition of absolute value

Definition of absolute value: The absolute value of a number is the distance the number is from zero. Take a look at the following two graphs:

Absolute value of 6 and -8
The first graph shows 6 located at a distance of 6 units from zero.
Then, the absolute value of 6 is 6 and we write |6| = 6

The second graph shows -8 located at a distance of 8 units from zero.
Then, the absolute value of -8 is 8 and we write |-8| = 8.

You can see from this that the absolute value of a number is always positive with the exception of taking the absolute value of 0 (|0| = 0)

Therefore, do not write |5| = -5 or |4| = -4 please!

|6| means distance from 0 to 6.

|-8| means distance from 0 to -8.

For |-8| = 8, you could also argue that to get 8, you have to take the negative of -8 since - - 8 = 8

So, | - 8| = - - 8 = 8.

This observation helps us to come up with a formal definition of absolute value.

| x | = x if x is positive or zero, but -x if x is negative.

This definition is important to understand before solving absolute value equations or absolute value inequalities.

Other examples helping us to apply the definition of absolute value

Calculate the absolute value of the following numerical expressions.

1) -8 + 2 × 5

2) 42 − 4 × 2

3) -5 + 5 × 2 − 15

1)

| -8 + 2 × 5 | = | -8 + 10 |

| -8 + 2 × 5 | = | 2 |

| -8 + 2 × 5 | = 2

2)

| 42 − 4 × 2| = | 16 − 4 × 2|

| 42 − 4 × 2| = | 16 − 8|

| 42 − 4 × 2| = | 8 |

| 42 − 4 × 2| = 8

3)

|-5 + 5 × 2 − 15| = | -5 + 10 − 15 |

|(-5 + 5 × 2 − 15)| = | 5 − 15 |

|(-5 + 5 × 2 − 15)| = | -10 |

|(-5 + 5 × 2 − 15)| = 10

Recent Articles

  1. How To Find The Factors Of 20: A Simple Way

    Sep 17, 23 09:46 AM

    Positive factors of 20
    There are many ways to find the factors of 20. A simple way is to...

    Read More

  2. The SAT Math Test: How To Be Prepared To Face It And Survive

    Jun 09, 23 12:04 PM

    SAT math
    The SAT Math section is known for being difficult. But it doesn’t have to be. Learn how to be prepared and complete the section with confidence here.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes