Question

Why does `|x|=-x` as `x -> -oo`?

I don't really see why.

If x is a negative number shouldn't the absolute value of that number be it's exact opposite?

Answer 1

That's how the modulus function is defined.

Explanation:

The function `|x|` is defined to be equal to `x` as long as `x` is positive (or zero), and `-x` when `x<0`. This means that `|x|=-x` is true as long as `x` is negative, not just as `x to -infty`.

Note that when `x=-3`, for example, `-x` is +3 - the "size" of the number `x`.