Question

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.

Answer 1

ok i will do it

Answer 2

|x| is also known as absolute value of x or modulus x

Answer 3

Now modulus x is a function that is always positive, that is it is always greater than zero..
\[\left| x \right| > 0\]

Answer 4

so for a positive function the function doesnt change.

Let us take an example.. Say x=5

so |5| = 5

Answer 5

Now for a negative function, the function just changes the sign, that is negative sign becomes positive

Answer 6

For eg. we have x= -5
|-5| = 5

Answer 7

Now if you see the graph of x looks like

Answer 8

for modulus x the function looks like

Answer 9

As it is always positive

Answer 10

Does this help?

Answer 11

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

Answer 12

We have given the user a complete research on modulus... Hope it helps :)

Answer 13

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)

Answer 14

When x is less than zero

Answer 15

negatives always make my brain go twisty...but thank you it did help clear up some confusion.

Answer 16

Yea many people find it confusing, the best way to tackle it is an example :D This method always works :)

Answer 17

If you need you can clear ALL your confusion

Answer 18

Just tell what is that is confusing you?