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The absolute value of a number is a measure of the size of that number.  The absolute value of <math>x</math> is written <math>|x|</math>.  If <math>x</math> is a positive number, then <math>|x| = x</math>.  If <math>x</math> is a negative number, then <math>|x| = -x</math>.  If <math>x=0</math> then <math>|x| = 0</math>.

The absolute value of a number is a measure of the size of that number.  The absolute value of <math>x</math> is written <math>|x|</math>.   

 

:If <math>x</math> is a positive number, then <math>|x| = x</math>.   

 

:If <math>x</math> is a negative number, then <math>|x| = -x</math>.   

 

:If <math>x=0</math> then <math>|x| = 0</math>.

Absolute value has several useful properties.  One is the ''multiplicative'' property.  If <math>x</math> and <math>y</math> are two numbers, then <math>|xy| = |x| \times |y|</math>.  Another is the ''triangle inequality'', which is the fact that <math>|x+y| \leq |x| + |y|</math>.  For example, if <math>x = 3</math> and <math>y = -5</math>, then <math>|x+y| = |3 + (-5)| = |3 - 5| = |-2| = 2</math>, while <math>|x| + |y| = |-5| + |3| = 5 + 3 = 8</math>.  In this case, the triangle inequality is the fact that 2 is not more than 8.

Absolute value has several useful properties.  One is the ''multiplicative'' property.  If <math>x</math> and <math>y</math> are two numbers, then <math>|xy| = |x| \times |y|</math>.  Another is the ''triangle inequality'', which is the fact that <math>|x+y| \leq |x| + |y|</math>.  For example, if <math>x = 3</math> and <math>y = -5</math>, then <math>|x+y| = |3 + (-5)| = |3 - 5| = |-2| = 2</math>, while <math>|x| + |y| = |-5| + |3| = 5 + 3 = 8</math>.  In this case, the triangle inequality is the fact that 2 is not more than 8.