[tex]|3-|x-2||\leq1[/tex]

x>=2  |3-x+2|<=1  |5-x|<=1   x>=5  x-5<=1  x<=6  [5;6]

                                             x<5   5-x<=1  x>=4  [4;5]    [4;6]

x<2    |3-2-x|<=1  |-x-1|<=1   |x+1|<=1

                                               x<-1  -x-1<=1  x>=-2  [-2;-1]

                                               x>=-1 x+1<=1  x<=0   [-1;0]    [-2;0]

[-2;0] U [4;6]