SOLUTION: If a, b, x, and y are all greater than 0 and x>a and y <b, how does x/y compare to a/b? Justify your answer.

SOLUTION: If a, b, x, and y are all greater than 0 and x>a and y <b, how does x/y compare to a/b? Justify your answer.

Algebra.Com

Question 1019960: If a, b, x, and y are all greater than 0 and x>a and y
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Assume that you have two positive numbers

and

and you calculate their product. Then you have another pair of positive numbers

and

where

and

. It should be obvious to the casual observer that:

for all positive real numbers

,

,

, and

such that

and

.

Since all the number are non-zero and non-negative, we can divide by any of them without creating an undefined number or changing the sense of the inequality. Divide both sides by

and

yielding:

for all positive real numbers

,

,

, and

such that

and

.

John

My calculator said it, I believe it, that settles it

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