To solve the equation, we first need to combine the fractions on the left side:

17/18 - x + 12/18 = 13 7/18
17/18 + 12/18 - x = 13 7/18
29/18 - x = 13 7/18

Next, we need to convert the mixed number on the right side to an improper fraction:

7/18 = 18/18 + 7/18 = 25/18

Now, our equation becomes:

29/18 - x = 13 + 25/18
29/18 - x = 234/18 + 25/18
29/18 - x = 259/18

To solve for x, we need to move the x term to one side of the equation:

x = 29/18 - 259/18
x = -230/18
x = -115/9

Therefore, the solution to the equation is x = -115/9.