To solve for \( x \) in the equation
\[ \frac{11}{4}x + 9 = 31, \]
follow these steps:
- Subtract 9 from both sides:
\[ \frac{11}{4}x + 9 - 9 = 31 - 9 \]
This simplifies to:
\[ \frac{11}{4}x = 22. \]
- Next, multiply both sides by the reciprocal of \(\frac{11}{4}\), which is \(\frac{4}{11}\):
\[ x = 22 \times \frac{4}{11}. \]
- Simplify the right side:
\[ x = \frac{88}{11} = 8. \]
Thus, the solution is
\[ \boxed{8}. \]
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