To solve the equation 3x - |x-1/2| = 3, we need to consider two cases: when x-1/2 is positive and when x-1/2 is negative.

Case 1: x-1/2 is positive
In this case, the absolute value of x-1/2 is equal to x-1/2. Therefore, the equation becomes:
3x - (x-1/2) = 3
3x - x + 1/2 = 3
2x + 1/2 = 3
2x = 3 - 1/2
2x = 5/2
x = (5/2) / 2
x = 5/4

Case 2: x-1/2 is negative
In this case, the absolute value of x-1/2 is equal to -(x-1/2). Therefore, the equation becomes:
3x - (-(x-1/2)) = 3
3x + x - 1/2 = 3
4x - 1/2 = 3
4x = 3 + 1/2
4x = 7/2
x = (7/2) / 4
x = 7/8

So the solutions to the equation 3x - |x-1/2| = 3 are x = 5/4 and x = 7/8.