To solve the equation \( \frac{1}{3} (6x - 9) = -33 \), we can follow the steps below:
Step 1: Eliminate the fraction.
Multiply both sides of the equation by 3 to get rid of the fraction:
\[ 3 \cdot \frac{1}{3} (6x - 9) = 3 \cdot -33 \]
This simplifies to:
\[ 6x - 9 = -99 \]
Step 2: Isolate the term with \( x \).
Add 9 to both sides of the equation to move the constant term:
\[ 6x - 9 + 9 = -99 + 9 \]
This simplifies to:
\[ 6x = -90 \]
Step 3: Solve for \( x \).
Divide both sides of the equation by 6 to isolate \( x \):
\[ x = \frac{-90}{6} \]
This simplifies to:
\[ x = -15 \]
Thus, the solution to the equation \( \frac{1}{3} (6x - 9) = -33 \) is \( x = -15 \).
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