# What is absolute value ? Definition and examples.

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

The distance 4 is from 0 is 4. You can write this as |4| = 4

The distance -4 is from 0 is 4. You can write this as |-4| = 4

Basically, the distance 4 is from 0 = absolute value of 4 =  |4| = 4

The distance -4 is from 0 = absolute value of -4 =  |-4| = 4

Generally speaking, distance x is from 0 = absolute value of x = |x|

However, what is |x| equal to ?

To answer this, you must make an important observation.

When we examine |4| = 4 and |-4| = 4, we see that the answer is positive.

When the number inside of || is positive, the answer is just the number.

However, when the number inside of || is negative, the answer is not -4, but -(-4) which is the same as 4.

## Formal definition of the absolute value

|x|  = { x is x is positive or -x if x is negative }

For example,

|6| = 6 since x = 6 and 6 is positive.

|-6| = -( -6) = 6 since x = -6 and -6 is negative.