To solve this equation for x, we will first simplify the expression on the left side of the equation:

1/4 (3/4 x - 1/2) + 2/5 = 1/2
= 1/4 3/4 x - 1/4 1/2 + 2/5 = 1/2
= 3/16 x - 1/8 + 2/5 = 1/2

Next, we will combine the constant terms on the left side of the equation:

3/16 x - 1/8 + 2/5 = 1/2
= 3/16 x + 5/40 - 8/40 = 20/40
= 3/16 x - 3/40 = 20/40
= 3/16 x = 23/40
= x = (23/40) * (16/3)
= x = 23/75

Therefore, the solution to the equation is x = 23/75.