read
this, which, coincidentally, is posted on a thread about this very problem.
the rule is simple, actually:
* if you multiply an inequality by a POSITIVE NUMBER on both sides, you change nothing about the inequality sign.
* if you multiply an inequality by a NEGATIVE NUMBER on both sides, you flip the inequality sign (i.e., "<" becomes ">" & vice versa, and "
<" becomes "
>" & vice versa).
if you don't know the sign of the quantity by which you're multiplying, then you can't do it at all, because of the consequences of these principles: you simply don't know what should happen to the inequality sign.