Absolute Value

The concept of absolute value has many uses, but you probably won't see anything interesting for a few more classes yet. There is a technical definition for absolute value, but you could easily never need it. For now, you should view the absolute value of a number as its distance from zero.


 

Let's look at the number line:

The absolute value of x, denoted "| x |" (and which is read as "the absolute value of x"), is the distance of x from zero. This is why absolute value is never negative; absolute value only asks "how far?", not "in which direction?". This means not only that | 3 | = 3, because 3 is three units to the right of zero, but also that | –3 | = 3, because –3 is three units to the left of zero.

Warning: The absolute-value notation is bars, not parentheses or brackets. Use the proper notation; the other notations do not mean the same thing.It is important to note that the absolute value bars do NOT work in the same way as do parentheses. Whereas –(–3) = +3, this is NOT how it works for absolute value:

• Simplify –| –3 |.

Given –| –3 |, I first handle the absolute value part, taking the positive and converting the absolute value bars to parentheses:
–| –3 | = –(+3)
Now I can take the negative through the parentheses:
–| –3 | = –(3) = –3

As this illustrates, if you take the negative of an absolute value, you will get a negative number for your answer.