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ALGEBRAIC DEFINITION OF ABSOLUTE VALUE

Click here for a brief discussion of the algebraic definition of absolute value.

Algebraic Definition of Absolute Value

| x | = { x , if    x≥0 x , if    x<0

That is, the absolute value of a number is itself, if the number is nonnegative.
The absolute value of a number is its opposite, if the number is negative.

The absolute value makes a useful appearance in the following formula:

For all real numbers  x ,

x 2=| x| .

That is, the square root of  x2  is the nonnegative number which, when squared, gives  x2 .
Note that   (-5) 2 =25= 5 , NOT  -5 !

EXAMPLES:
Let  x = 3 .  Then,   |x| = x .
Let  x = -3 .  Then,   |x| = -x .
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Answer this question:


x
-x




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Algebra II Table of Contents

One Mathematical Cat, Please! A First Course in Algebra
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