Can anyone explain absolute values to me. The definition my teacher gave was a bit confusing |x|=x if x is greater than or equal to and |x|= -x if x is less than zero. I thought absolute value was just the distance x was from zero so it couldn't end up negative.

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Can anyone explain absolute values to me. The definition my teacher gave was a bit confusing |x|=x if x is greater than or equal to and |x|= -x if x is less than zero. I thought absolute value was just the distance x was from zero so it couldn't end up negative.

Mathematics
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ok i will do it
|x| is also known as absolute value of x or modulus x
Now modulus x is a function that is always positive, that is it is always greater than zero.. \[\left| x \right| > 0\]

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so for a positive function the function doesnt change. Let us take an example.. Say x=5 so |5| = 5
Now for a negative function, the function just changes the sign, that is negative sign becomes positive
For eg. we have x= -5 |-5| = 5
Now if you see the graph of x looks like|dw:1326414074983:dw|
for modulus x the function looks like |dw:1326414124726:dw|
As it is always positive
Does this help?
I would like to add that the statement |x| = -x when x < 0 means that for example: Lets say x = -2 so it's less than zero. |-2| = -(-2) Absolute value of -2 is the opposite of -2 which is 2
We have given the user a complete research on modulus... Hope it helps :)
I enjoyed your explanation =) I've seen the confusion with the |x| = -x before (Which should be read as absolute value of x is the opposite of x)
When x is less than zero
negatives always make my brain go twisty...but thank you it did help clear up some confusion.
Yea many people find it confusing, the best way to tackle it is an example :D This method always works :)
If you need you can clear ALL your confusion
Just tell what is that is confusing you?

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