1. The problem statement, all variables and given/known data Show the following for every d>0: For every real number x with |x-1|<d it follows that |1+x|<2+d 2. The attempt at a solution If x-1>0, then |x-1|=x-1<d. Hence x+2 = |x+2| < 2+d. If x-1<0, then |x-1|=-(x-1)<d. Hence x-1>-d => x+1 > 2-d ...?? Is this really possible to do without putting any other restrictions on d?