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 ->
Expressions-with-variables
-> 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.
Log On
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
