Thanks then that would make sup S = 3 and inf S = 2, is that right?
But how did you get to S=[2,3] as with my equation above i couldn't get a sensible result for x
Why not consider each term separately?
Since |3-x| is non-negative, |x-2|<=1. Solve this to get 1<=x<=3. Since 3 is in the set, it's the supremum. Now do something similar with |3-x|.
I didn't mean that 1<=x<=3 is the solution set, but it's still true. |3-x|<=1 then gives 2<=x<=4, which gives the infinum. I didn't see your solution immediately so I went with the slightly longer one.