Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this?

A negative means opposite, therefore the inequality sign also recieves the action of the oppositte, so it swhiches.

Good question. This page gives a good explanation of why you have to change the direction:

http://mathforum.org/library/drmath/view/57874.htm...

You can prove it algebraically too. If x < y, then subtracting x from both sides gives you 0 < y - x. This means the same thing as -x + y > 0, then subtracting y from both sides gives you -x > -y. So if x < y, then -x > -y.

Think about 2>1

is -2>-1

technically it's because numbers express magnitude from zero whereas the sign expresses the magnitude from negative infinity