Inequalities

[Guest]

I have a problem understanding this concept of inequalities stated on page 80 of the module Equations, Inequalities and VICs

I am havign difficulties understadnign this rule Do not multiply or divide inqequalities by unknowns (unless you know the sign)
the example illustrated in the same says xy< 3y, what is the range of possible values for x

and it says we do not know if x is negative or positive....
my query is in the same example if xy is positive then the two possible options are that both are positive or both are negative... again the inequality is compared between positve xy and positive 3y, means both again which means the sighs of both 3 and y must be the same as x and y....so either both are positive and or both are negative....why cant i determine the signs this way.....please help

[rfernandez]

Actually, the text says that we don't know whether y is positive or negative, and that's the problem. One way to show this is to plug in values for y and see what happens.

Suppose y = 4:

xy < 3y
4x < 12
x < 3

Now, suppose y = -4:

-4x < -12
x > 3

So, depending on the sign of y, we get different ranges of possible values of x.

I think you're making an incorrect assumption about xy. In fact, xy could be either positive or negative -- it's not true that the product xy must be positive.