4/9 (2.7y - (2 + 1/4)) - 4.2 (5/7y - 0.5x)

First, simplify the expression within the parentheses:
2.7y - (2 + 1/4) = 2.7y - 2 - 1/4
= 2.7y - 2 - 0.25
= 2.7y - 2.25

Now substitute back into the original expression:
4/9 (2.7y - 2.25) - 4.2 (5/7y - 0.5x)

Multiplying the factors inside the parentheses:
4/9 2.7y - 4/9 2.25 - 4.2 5/7y + 4.2 0.5x
= 1.6y - 1 - 3y + 2.1x (solving each part separately)

Now combine like terms:
1.6y - 3y = -1.4y
-1 - 2.1 = -3.1

Final simplified expression:
-1.4y - 3.1