Answer
In the step "Multiply both sides by y-x"
we are multiplying with a negative number, so the inequality should have changed from $\gt$ to $\lt.$
(please see step by step for the correction)
Work Step by Step
$...$
$ 2(y-x)\lt 1(y-x) \qquad $multiply with y-x, which is negative
$ 2y-2x\lt y-x \qquad$ use distributive property
$ y-2x\lt -x \qquad$subtract y from both sides
$ y\lt x \qquad$ add 2x to both sides
which is true, because we were given $x\gt y$.
