GMAT Data Sufficiency (DS) | Re: Is |x-1| < 1?

Hi,

I got the right answers as my final equations however, I chose D instead of E. For S1, I got x= 0 or 2. If you plug these two in the original equation, you can "no" as an answer which I thought was sufficient. For S2, I got x= -1 or 1. Again, I plugged both of these numbers in and got "no" as an answer as well. Could anyone please explain how both of these equations are insufficient even when we are getting "no" as an answer? Please help!