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Some of the content of this guide was modeled after a guide originally created by the Openstax and has been adapted for the GPRC Learning Commons in September 2020. This work is licensed under a Creative Commons BY 4.0 International License .

Absolute Value

Absolute Value:

The absolute value of x, represented by |x|, is the distance between zero and x on a number line. Since distance can never be negative, absolute value of x is always positive. For example, |-5| is the distance of -5 from zero. Note that we do not need to know in which direction -5 is from zero. Since -5 is 5 units away from zero, therefore |-5|=5. 
Example 1: Simplify -|-6|+|-2|.
It is easier to solve this problem step by step:
Step 1) We find the value of -|-6|: we know that the output of an absolute value function is always positive, so, |-6|=6. Therefore, we have -|-6|=-6.
Step 2) We also find: |-2|=2.
Step 3) Using the steps above, -|-6| + |-2| = -6+2 = -4.


Example 2: Simplify |-4|(7-|-8|).
Step 1) We simplify inside the bracket: (7-|-8|)=7-8=-1.
Step 2) We then simplify |-4|(-1)=4(-1)=-4.


Example 3: Simplify |-12||-3|.
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