To solve the equation \( \frac{1}{3}x = -9 \) using inverse operations, follow these steps:
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Identify the operation on \( x \): Here, \( x \) is being multiplied by \( \frac{1}{3} \).
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Use the inverse operation: The inverse of multiplying by \( \frac{1}{3} \) is multiplying by its reciprocal, which is 3.
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Multiply both sides by 3:
\[ 3 \cdot \left( \frac{1}{3}x \right) = 3 \cdot (-9) \]
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Simplify both sides:
\[ x = -27 \]
Thus, the solution to the equation \( \frac{1}{3}x = -9 \) is:
\[ x = -27 \]
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