0

|x-3|

If x is less than 3, will |x-3| be negative? I don't think so.

For example, if x=2, |x-3|= |2-3|=1. x-3 can never be negative, I think.

In this link, it has been said that when x<3, x-3 is negative, thus |x-3|=-(x-3).

enter image description here

I think this statement is totally wrong.

Please let me know what the correct is.

user64814
  • 51
  • 1
    If $x$ is less than three then $x-3$ is negative, and $|x-3| = -(x-3)$ is positive. – What exactly do you think is “totally wrong”? – Martin R May 07 '21 at 14:28
  • 3
    Just because something has a minus sign in front of it that doesn't make it "negative." – Randall May 07 '21 at 14:29
  • Also, just take a concrete case to see what's going on. What's the absolute value of $-3$? According to the definition, it is $-(-3)=3$, which is positive. – Randall May 07 '21 at 14:31

2 Answers2

1

$|x|$ is non-negative regardless of any sign. Absolute value is the distance of a number from $0$ and distance can never be negative!

p_square
  • 1,007
  • 1
  • 6
  • 23
0

The statement is correct because if x is lesser than 3 , the x -3 is always negative and hence -(x-3) is always positive. And that is always equal to mod x-3

Jayaram Iyer
  • 119