To solve this equation, we need to combine the fractions on the left side of the equation and simplify.

1) Finding a common denominator for the fractions:

The denominators are 9x, 18x, and 27x. The least common multiple of these three numbers is 9x * 2 = 18x.Rewrite each fraction with the common denominator:
1\9x = 2\18x
7\18x = 1\2 7 = 7\2
11\27x = 2\18x 11\3 = 22\18x

Now we have the equation:
2\18x + 7\2 - 22\18x = 2 1\2

2) Combine the fractions:
2\18x - 22\18x = -20\18x = -10\9x
-10\9x + 7\2 = -10\9x + 63\18x = -10\9x + 63\18x = -7\6x

Now the equation becomes:
-7\6x = 2 1\2

3) Solve for x:
-7\6x = 2 1\2
-7\6x = 2\1/2
-7\6x = 5\1/2
x = (5\1/2) / -7\6
x = -11/4

Therefore, the solution to the equation is x = -11/4.