I'm trying to solve 1/(2-x) > 1/2 for x, where 0 < x < 1. The problem is, I'm getting x < 0 where as I think it should be x > 0. I know you need to flip the inequality when multiplying or dividing by a negative number, but this isn't coming up at all. What am I missing?

1/(2-x) > 1/2 Since 0 < x < 1, (2-x) is never negative and multiplying by it does not switch the inequality

2 > 2 - x

0 > x