To solve this equation, we need to distribute and combine like terms:

2/3(1.5x + 0.6) - 0.8(5/12x - 0.5) = 1

First, distribute the constants:

(2/3)(1.5x) + (2/3)(0.6) - (0.8)(5/12x) + (0.8)(0.5) = 1

Simplify the expression:

1x + 0.4 - 1/3x + 0.4 = 1

Combine like terms:

1x - 1/3x + 0.4 + 0.4 = 1

Now, combine the x terms:

1 - 1/3 = 1

0.67x = 1

To solve for x, divide both sides by 0.67:

x = 1 / 0.67

x ≈ 1.49

Therefore, the solution to the equation is x ≈ 1.49.