To solve this equation, we need to first simplify the left side of the equation by combining like terms:

(х - 5 1/2) + 7 5/18 = 9 4/9

First, convert 7 5/18 to an improper fraction:

7 5/18 = (7 * 18 + 5) / 18 = 131/18

Now the equation becomes:

(х - 11/2) + 131/18 = 85/9

Next, find a common denominator to combine the fractions:

Multiply 9 by 18 to get a common denominator of 162:

18(х - 11/2) + 9(131/18) = 9(85/9)

Now, rewrite the equation with the common denominator:

18x - 99 + 131 = 170

Combine like terms:

18x + 32 = 170

Subtract 32 from both sides:

18x = 138

Divide by 18 to solve for x:

x = 138/18

x = 23/3

Therefore, the solution to the equation is x = 23/3.