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.
|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.
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