+129852 I remember this one from awhile back......one of our really good members [hectictar ] showed me the solution
I believe the problem is as follows :
1 5
0 > ________ > 1 - ___
1 -10/x y
1 5
________ > 1 - ___
1 -10 / x y
x 5
_______ - 1 > - _____
x -10 y
x - (x -10) 5
__________ > - ___
x - 10 y
10 5
_______ > - ______
x -10 y
And we know 0 < x < 10 because that is the only way 1 / [ 1 -10/x ] can be less than 0.
Since x - 10 is negative, when we multiply both sides by it, we flip the sign.
10 < - 5 ( x -10)
___________
y
And we know 0 < y < 5 because that is the only way that 1 - 5/y can be less than 0
So
Since y is positive, when we mult both sides by it, don't flip the sign.
10 y < - 5(x - 10) this leads to
y < 10 - x
________
2
y < (-1/2)x + 5
So
We have these three inequalities
0 < x < 10
0 < y < 5
y < (-1/2)x + 5
And the intersection of these forms the lower-left triangle area , here :
https://www.desmos.com/calculator/y1vjodjezc
I'll let you find the integer solutions in this area ....
THANKS TO HECTICTAR FOR THIS SOLUTION !!!!!
