Let's solve the equation step by step:

Distribute the negative sign in the parentheses:
1 3/4 - 0.7 + 2.5x = 1.17

Combine like terms:
1 3/4 - 0.7 = 1 3/4 - 7/10 = 7/4 - 7/10 = 35/20 - 14/20 = 21/20

So the equation becomes:
21/20 + 2.5x = 1.17

Simplify the equation by converting 1.17 to an improper fraction:
1.17 = 117/100

Now the equation becomes:
21/20 + 2.5x = 117/100

Solve for x:
2.5x = 117/100 - 21/20
2.5x = 117/100 - 42/20
2.5x = 117/100 - 84/100
2.5x = 33/100

x = 33/100 / 2.5
x = 33/100 * 1/2.5
x = 33/250

Now we move on to the second part of the equation:

1 1/9 (3x + 0.9) = 4 1/3
1 1/9 (33/250 + 0.9) = 13/3
10/9 (33/250 + 9/10) = 13/3
10/9 (33/250) + 10/9 9/10 = 13/3
330/2250 + 10/9 9/10 = 13/3
330/2250 + 1 = 13/3
330/2250 + 1 = 117/9
330/2250 = 117/9 - 9/9
330/2250 = 108/9
330/2250 = 12/1

After solving both parts of the equation, we find that x = 33/250 and is equal to 12.