Absolute Value question

[maia]

In OG 11 absolute value |x| is defined as distance between number x and 0 on the line number so |-3| = 3 and |3| = 3.

It is also defined as |x| = x if x >=0 and |x| = -x if x < 0 . So |-3| = -3 and |3| = 3 ??

Math gurus, What is correct?

Thanks
Maia

[chayanika]

Modulus of any number is always positive because it is the absolute size of the number. That is we disregard any sign it might have. That makes |x|=x and |-x| = x. Similarly |3|=3 and |-3| = 3

But to get the modulus of a negative number we need to multiply the number by -1, for example -1*(-3 )

Hence we can generalise the above finding by saying that to get modulus of positive number (x) we can directly write x while to get the modulus of a negative number we need to multiply by -1*x = -x

Therefore, |x| = {x, if x is positive and -x if x is negative}