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 numberless than1? You get an answer that isless thanforpositive. 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 alargernumber.

This means that for negative .

Or, " for all " is to say the same thing.

So, regardless of the value for ,