To solve this equation, we need to isolate the variable x on one side of the equation.

Starting with the equation:

7 + 9x/4 + 2x - x/9 = 7x + 1

First, let's combine like terms:

(9/4)x - (1/9)x + 2x - 7x = 7 - 1

Simplify further:

(9/4 - 1/9)x + 2x - 7x = 6

Now, find a common denominator for (9/4 - 1/9):

(81/36 - 4/36)x + 2x - 7x = 6

(77/36)x - 5x = 6

(77/36 - 180/36)x = 6

(77 - 180)/36)x = 6

-103/36(x) = 6

Multiply both sides by -36/103 to solve for x:

x = -6 * 36 / 103

x = -216 / 103

Therefore, the solution to the equation is x = -216/103.