To solve the equation \(\frac{1}{3}x = -9\) using inverse operations, follow these steps:
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Multiply both sides by 3 to eliminate the fraction:
\[ 3 \cdot \left(\frac{1}{3}x\right) = 3 \cdot (-9) \]
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This simplifies to:
\[ x = -27 \]
So, the solution is:
\[ \boxed{-27} \]