To solve the equation \( \frac{14}{7 - x} = 3 \), follow these steps:
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Isolate the fraction: The equation is already set up as \( \frac{14}{7 - x} = 3 \).
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Eliminate the fraction: Multiply both sides of the equation by \( 7 - x \) to get rid of the denominator: \[ 14 = 3(7 - x) \]
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Distribute the right-hand side: \[ 14 = 21 - 3x \]
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Rearrange the equation: To isolate \( x \), move \( 3x \) to the left side and 14 to the right side: \[ 3x = 21 - 14 \] \[ 3x = 7 \]
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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 is \[ x = \frac{7}{3}. \]
You can also verify your solution by substituting \( x = \frac{7}{3} \) back into the original equation and ensuring both sides are equal.
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