2<(5-2x)<7 the problem

2-5<-2x<7-5
-3/2<-2x<2/2
-3/2<x<1

I feel like I have done something wrong with this problem.

Remember - whenever you multiply or divide through by a negative number, you have to flip the inequality symbols around. Thus:

-3/2 < -x < 2/2
3/2 > x > -1