Not sure I understand your confusion.
Do you understant that as , then, for positive ,
You could conceptualize it this way:
So what happens when you multiply by a number less than 1? You get an answer that is less than for positive . And as , then, for positive and positive , you you can conclude that:
. The absolute value signs are included because the opposite is true for negative numbers:
...so multiplying a negative number by a number less than gives you a larger number.
This means that for negative .
Or, " for all " is to say the same thing.
So, regardless of the value for ,