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

1/9x + 7/18x - 11/27x can be combined by finding a common denominator. The common denominator for 9, 18, and 27 is 27.

So, we rewrite the equation with the common denominator:

(3/27)x + (7/27)x - (11/27)x = 2 1/2

Now, we can add the fractions:

(3/27 + 7/27 - 11/27)x = 2 1/2
(-1/27)x = 2 1/2

To solve for x, we need to multiply both sides by -27:

x = -27 2 1/2
x = -27 5/2
x = -135/2

Therefore, the value of x is -135/2.