Word Translations 4th Edition

[isamumassey]

My question is from page 21 of the 4th edition Word Translations strategy guide, the "dropping negative possibilities w/ inequalities" table:

In the "cross-multiplying" row, the guide states that when (x/y)<(y/x), (x^2)<(y^2) if you are told that x>0 and y>0.

However, in this instance, isn't (x^2)<(y^2) whenever x and y are the same signs, not just when x and y are both greater than 0? (Because if they're both negative you would just flip the inequality twice.) Am I missing something here?

[jnelson0612]

Hi there,
I completely agree with you. If both x and y are positive you don't have to worry, and if they are both negative you will flip the sign when you multiply one of them across and then flip it back when you multiply the other one. The only scenario to be really concerned about is when one is positive and the other is negative. Very good catch!