Solve the equation [3x + 1] = 2x-0.5, where [] is the integer sign

Solve the equation [3x + 1] = 2x-0.5, where [] is the integer sign

Let 2x - 0.5 = y, if y is positive, then 3x + 1 is constant > 2x - 0.5, so y is negative
When y is negative,
3*(y+0.5)/2+1