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# inequality problem

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we have (x, y) with 0

$$\frac{1}{1-\frac{10}{x}}>1-\frac{5}{y}$$

how many pairs of integers (x, y) satisfy the inequality?

with casework i got 12 but it is wrong.

how do i solve?

Guest Aug 2, 2018
#1
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doing some simplifing, we get

y> (-x+10)/2

without defining any limits to x or y

the answer is infinite because lets say x= anything over 10

then any y >0 would be positive and greater than our negative on the other side

Guest Aug 7, 2018