To solve the equation \( \frac{3}{x-7} = 6 \), follow these steps:
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Multiply both sides by \( x-7 \) (to eliminate the fraction):
\[ 3 = 6(x - 7) \]
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Distribute the 6 on the right side:
\[ 3 = 6x - 42 \]
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Add 42 to both sides:
\[ 3 + 42 = 6x \]
\[ 45 = 6x \]
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Divide both sides by 6:
\[ x = \frac{45}{6} \]
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Simplify the fraction:
\[ x = \frac{15}{2} \quad \text{or} \quad x = 7.5 \]
Thus, the solution is:
\[ x = \frac{15}{2} \quad \text{or} \quad x = 7.5 \]