The absolute value of a number is its distance from zero on the number line. The absolute value of a number
x is denoted by
|x|.
Lets take for example the problems |4| and |-4|. On a number line we can see that both numbers are 4 spaces away from 0.
Since they are both 4 spaces away from 0, the absolute value of 4 is 4 and the absolute value of -4 is also 4.
|4| = 4
|-4| = 4
Absolute Values and Variables
When dealing with absolute values and variables, it is important to remember that the variable is an unknown and could be either positive or negative. We must take this into account when dealing with an expression such as |x|. If we were to evaluate this expression and x = 0 then we can say that |x| = x, however lets say that x = -3. If |x| = x were to hold true for all values of x, then we would have the following:
|-3| = -3
We know this not to be the case as an absolute value cannot be negative. What we can say is that |x| = -x, which would hold true as seen below:
|-3| = -(-3) = 3
We must define the absolute value of x or |x| in pieces:
More Examples
|3 -7| = |-4| = 4
|0| = 0
|3(2)| = |6| = 6