I hate DS inequalities questions with a passion. At the moment, my only workable, quick way of solving these is to try to sketch the inequalities and look for areas of overlap. I can manage algebraic solutions if I have plenty of time or the question is easy. Generally I don't like algebra with inequalities because the range of possible manipulations seems smaller, and I can't see how to get to my target expression.
Aaaanyway, I was looking at this:
https://www.beatthegmat.com/equality-t30669.html
If r + s > 2t, is r > t ?
(1) t > s
It occurred to me that, given (1), I should be allowed to substitute the "s" in the first equation for "t", since this preserves the inequality, and get
r + s > 2t
=> r + t > 2t
=> r > t
and for the second part
2) r > s
can I substitute:
r + s > 2t
=> 2r > 2t
=> r > t
Sorry if this is an obvious question, but it's not something I remember reading or learning anywhere, but it seems reasonable so long as I preserve the inequality (i.e. make the big side bigger or the small side smaller)
Is this a reliable method of manipulation? Is this well taught in any of the books or on any website?
Aaaanyway, I was looking at this:
https://www.beatthegmat.com/equality-t30669.html
If r + s > 2t, is r > t ?
(1) t > s
It occurred to me that, given (1), I should be allowed to substitute the "s" in the first equation for "t", since this preserves the inequality, and get
r + s > 2t
=> r + t > 2t
=> r > t
and for the second part
2) r > s
can I substitute:
r + s > 2t
=> 2r > 2t
=> r > t
Sorry if this is an obvious question, but it's not something I remember reading or learning anywhere, but it seems reasonable so long as I preserve the inequality (i.e. make the big side bigger or the small side smaller)
Is this a reliable method of manipulation? Is this well taught in any of the books or on any website?
80% of success is showing up -- Woody Allen
