Inequalities - Cross Multiplying to Simplify?

[gxj007]

Hi -

I was working through the last set of DS problems #145 in OG 11 and was attempting to cross multiply in order to simplify the equation for an inequality, however, according to the answer it doesn't seem like this works? Is it safe to say that for inequalities you can can not cross multiply to simplfy. I'm assuming this stems from not knowing if a variable is positive or negative.

Is 1/P > r/(r^2+2)


Any thoughts?

thanks!

[Osirus@VeritasPrep]

You can't cross multiply with inequalities when using variables because if one of the variables is negative then the sign would change. Since you don't have the value of the variable, if you cross multiply you would not know whether or not leaving the sign as it is would still make the expression correct. Hope that helps.

[gxj007]

perfect. thanks!

[rah_pandey]

However in your question you can cross multiply r^2+2 as it is always positive