To solve this equation, we will first distribute the 2/3 on the left side:

2/3 1/3x - 2/3 0.5 = 4x + 2.5
2/9x - 1/3 = 4x + 2.5

Next, we will combine like terms by subtracting 4x from both sides:

-1/3 - 4x = 2/9x + 2.5
-4 1/3x = 2/9x + 2.5

Now, we will get rid of the fractions by multiplying every term by 9:

9(-4 1/3x) = 9(2/9x) + 9*2.5
-37x = 2x + 22.5

Next, we will combine like terms by adding 37x to both sides:

-37x - 2x = 22.5
-39x = 22.5

Finally, we will solve for x by dividing both sides by -39:

x = -22.5 / 39
x = -0.57692307692

Therefore, the solution to the equation is x = -0.57692307692.