Solve for x . \[ \frac{3 x+5}{18}+\frac{3 x-7}{9}=x+6 \]

Let's solve the equation step by step. First, we'll rewrite the equation for clarity: \[ \frac{3x + 5}{18} + \frac{3x - 7}{9} = x + 6 \] To eliminate the fractions, we can find a common denominator. The common denominator for 18 and 9 is 18. We can rewrite the second term: \[ \frac{3x - 7}{9} = \frac{2(3x - 7)}{18} = \frac{6x - 14}{18} \] Now we can substitute this back into the equation: \[ \frac{3x + 5}{18} + \frac{6x - 14}{18} = x + 6 \] Combining the fractions on the left side: \[ \frac{(3x + 5) + (6x - 14)}{18} = x + 6 \] This simplifies to: \[ \frac{9x - 9}{18} = x + 6 \] Now simplify the left side: \[ \frac{9(x - 1)}{18} = x + 6 \implies \frac{x - 1}{2} = x + 6 \] Next, multiply both sides by 2 to eliminate the fraction: \[ x - 1 = 2(x + 6) \] Distributing the 2 on the right side: \[ x - 1 = 2x + 12 \] Now, isolate x by moving all x terms to one side and the constant terms to the other side: \[ x - 2x = 12 + 1 \] This simplifies to: \[ -x = 13 \implies x = -13 \] Thus, the solution for x is: \[ \boxed{-13} \]