To solve this expression, we follow the order of operations (PEMDAS).

3×1.5 + (4/9 - 6/5) ÷ 1 8/9

First, we simplify the terms inside the parentheses:

4/9 - 6/5 = (45 - 69) / (9*5)
= (20 - 54) / 45
= -34 / 45

Next, we simplify the division:

-34 / 45 = -34 ÷ 45 = -0.7556

Now, we substitute these values back into the expression:

3×1.5 + (-0.7556) ÷ 1 8/9
= 4.5 - 0.7556 ÷ 1 8/9

Finally, we perform the remaining operations:

4.5 - 0.7556 = 3.7444

Therefore, the solution is 3.7444.