If 0< |x- 2|< 2 then -2< x- 2< 2 (with ). Adding 2 to each part, 0< x< 4 (with ). Multiplying by 2, 0< 2x< 8 (with ). Subtracting 3, -3< 2x- 3< 5 (with 2x- 3\ne 1). That is, if 0< |x- 2|< 2, 2x- 3 can be any number strictly between -3 and 5, except 1.