To solve the equation \( \frac{14}{7 - x} = 3 \), follow these steps:
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Eliminate the Fraction: Multiply both sides of the equation by \( 7 - x \) to get rid of the fraction. Ensure that \( 7 - x \neq 0 \) (which would make the denominator undefined).
\[ 14 = 3(7 - x) \]
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Distribute the Right Side: Distribute the 3 on the right side of the equation.
\[ 14 = 21 - 3x \]
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Rearrange the Equation: To isolate the term with \( x \), move \( 3x \) to the left side and \( 14 \) to the right side.
\[ 3x = 21 - 14 \]
Simplifying the right side gives:
\[ 3x = 7 \]
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Solve for \( x \): Divide both sides by 3.
\[ x = \frac{7}{3} \]
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Conclusion: The solution to the equation \( \frac{14}{7 - x} = 3 \) is
\[ x = \frac{7}{3} \]
You can substitute \( x = \frac{7}{3} \) back into the original equation to verify that it is correct.