sam2304 wrote:
I went this way using both.
Divide 1 by 2. we get z/y > 1 => z > y since all are positive.
I've highlighted your mistake. You absolutely can NOT divide one inequality by another. You can see why this is not correct just using numerical examples. The following inequalities are both true:
4 > 2
3 > 1
but if we divide the first inequality by the second, the result is not true.
You certainly can divide one *equation* by another (though it isn't often useful to do that), at least as long as you're sure you're not dividing by zero. In fact, with equations we can combine them (add, subtract, multiply, divide, etc) in almost any way we like. That is certainly *not* the case for inequalities. With two inequalities, you can always safely add them together if they face the same way, though you'd only ever consider doing that in a question with at least 2 unknowns. You cannot safely subtract or divide (these are just wrong) inequalities, or even multiply them if negative numbers might be involved.