## gypsi 3 years ago 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.

1. Akshay_Budhkar

ok i will do it

2. Akshay_Budhkar

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

3. Akshay_Budhkar

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

4. Akshay_Budhkar

so for a positive function the function doesnt change. Let us take an example.. Say x=5 so |5| = 5

5. Akshay_Budhkar

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

6. Akshay_Budhkar

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

7. Akshay_Budhkar

Now if you see the graph of x looks like|dw:1326414074983:dw|

8. Akshay_Budhkar

for modulus x the function looks like |dw:1326414124726:dw|

9. Akshay_Budhkar

As it is always positive

10. Akshay_Budhkar

Does this help?

11. cazil

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

12. Akshay_Budhkar

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

13. cazil

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)

14. cazil

When x is less than zero

15. gypsi

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

16. Akshay_Budhkar

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

17. Akshay_Budhkar

If you need you can clear ALL your confusion

18. Akshay_Budhkar

Just tell what is that is confusing you?