First, let's simplify the fractions on both sides of the equation:

7 3/22 = (154 + 3) / 22 = 157 / 22
4 9/44 = (176 + 9) / 44 = 185 / 44
9 8/33 = (297 + 8) / 33 = 305 / 33
4 2/77 = (308 + 2) / 77 = 310 / 77

So the equation becomes:

(157/22 - x) + (185/44) = (305/33 - 310/77)

Now combine like terms:

157/22 - x + 185/44 = 305/33 - 310/77

To add fractions, we need to find a common denominator. The least common multiple of 22, 44, 33, and 77 is 924.

Multiplying the first fraction by 42/42, the second by 21/21, the third by 28/28, and the fourth by 12/12 to get the common denominator:

(15742/924 - 42x/924) + (18521/924) = (30528/924 - 31012/924)

Now add the fractions:

(6574/924 - 42x/924) + (3885/924) = (8540/924 - 3720/924)

Combine like terms:

(6574 - 42x + 3885) / 924 = (8540 - 3720) / 924

(10459 - 42x) / 924 = 4820 / 924

Now, multiply both sides by 924 to isolate x:

10459 - 42x = 4820

-42x = 4820 - 10459
-42x = -5649

Finally, solve for x:

x = 5649 / 42
x = 134.5

Therefore, the solution to the equation is x = 134.5.