Let's solve this step by step:

First, let's simplify the expression within the parentheses
1.5 + 3 = 4.5

Next, let's multiply 4.5 by 4/15
4.5 * 4/15 = 18/15 = 1.2

Now, let's simplify the expression within the second set of parentheses
$8/11$x - 3/7

Next, we multiply 0.77 by $8/11$x
0.77 * 8/11x = 6.16/11x

Then, we multiply 0.77 by -3/7
0.77 * -3/7 = -2.31/7

Now, we subtract -2.31/7 from 6.16/11x
6.16/11x - 2.31/7 = $42.76/77$x - 2.31/7 = $42.76x/77$ - $2.31/7$

Finally, we subtract step 2 from step 6
1.2 - $42.76x/77$ + $2.31/7$ = 1.2 - 42.76x/77 + 0.33

Therefore, the simplified expression is 1.2 - $42.76x/77$ + 0.33.