Why is -x the maximum of -x and x in the absolute value function?

[fission]

hi all so this is a very basic question i think and i feel very bad for tumbling here but still i need to clear this, so from childhood i was taught that the negative numbers are less than positive but now when i am studying limits and functions i came across absolute function and it said |-x| = max{-x,x}. alright seems legit but now the book says that max of the two is -x and that's why function came out positive due to double minus sign, so i want to ask how is -x greater than x or i am doing something wrong here? thanks for ur help

 

[mfb]

If x=-5, then -x=-(-5)=5 is larger than x=-5.

If x is negative, -x is larger than x, otherwise it is not.

 

[dkotschessaa]

It's just something that tricks your brain until you think about it for a second.

Q: Is $-x$ is a negative number?
A: Not necessarily.

You don't know what $x$ is. If $x = -3$ then $-x =-(-3) = 3$ which is positive.

I prefer to have the absolute value function written piecewise:

 

[fission]

duh! lol that was really a simple one xD but thanks everyone for giving a good explanation :)