Answer
The problem with this argument is that when you multiply both sides by (y-x) you are multiplying by a negative number (-x) therefore you must switch the direction of the sign. The correct solution is y$\lt$x.
Work Step by Step
2$\gt$1
2(y-x)$\lt$1(y-x)
2y-2x$\lt$y-x
y$\lt$x
