To solve the equation \(3x + 8x = 81 - \frac{34}{2} + 2\), we can simplify both sides step by step.
Combine like terms on the left side:
\[ 3x + 8x = 11x \]
Simplify the right side:
\[ 81 - \frac{34}{2} + 2 \] First, divide \(34\) by \(2\):
\[ \frac{34}{2} = 17 \]
Now plug this back into the right side:
\[ 81 - 17 + 2 = 81 - 17 = 64 \quad \text{and then} \quad 64 + 2 = 66 \]
Set the simplified equation:
\[ 11x = 66 \]
Solve for \(x\):
\[ x = \frac{66}{11} = 6 \]
Thus, the solution is:
\[ \boxed{6} \]