Find all real numbers x satisfying floor(x) + floor(2x) = floor(3x)
An arbitrary real x can be represented as n + x' where n is an integer and 0 <= x' < 1. Consider four cases so that in each case you know precisely between which integers 2x' and 3x' is located. E.g., The first case is 0 <= x' < 1/3; then 0 <= 2x' < 1 and 0 <= 3x' < 1.