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