To solve the equation \( 3 - \frac{6}{x} = -3 \), follow these steps:
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Start by isolating the term with \( x \). First, subtract 3 from both sides:
\[ -\frac{6}{x} = -3 - 3 \]
This simplifies to:
\[ -\frac{6}{x} = -6 \]
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Next, multiply both sides by -1 to eliminate the negative sign:
\[ \frac{6}{x} = 6 \]
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Now, cross-multiply to solve for \( x \):
\[ 6 = 6x \]
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Divide both sides by 6:
\[ x = 1 \]
Thus, the solution is:
\[ \boxed{1} \]