To solve the equation \( \frac{11}{4} x + 9 = 31 \), follow these steps:
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Start by isolating the term with \( x \). Subtract 9 from both sides:
\[ \frac{11}{4} x + 9 - 9 = 31 - 9 \] \[ \frac{11}{4} x = 22 \]
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Next, multiply both sides by the reciprocal of \( \frac{11}{4} \) to solve for \( x \). The reciprocal is \( \frac{4}{11} \):
\[ x = 22 \times \frac{4}{11} \]
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Simplify the right-hand side:
\[ x = \frac{22 \times 4}{11} \] \[ x = \frac{88}{11} \] \[ x = 8 \]
So, the solution is \( x = 8 \).