To solve the Celsius to Fahrenheit formula \( F = \frac{9}{5}C + 32 \) for \( C \), we can follow these steps:
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Subtract 32 from both sides: \[ F - 32 = \frac{9}{5}C \]
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Multiply both sides by \(\frac{5}{9}\) to isolate \( C \): \[ C = \frac{5}{9}(F - 32) \]
Thus, the formula for converting Fahrenheit to Celsius is: \[ C = \frac{5}{9}(F - 32) \]
Checks for True Answers:
- The computed formula correctly transforms Fahrenheit values back into Celsius.
- If you substitute an appropriate \( F \) into \( C = \frac{5}{9}(F - 32) \), it will yield the corresponding Celsius temperature.
To check whether this is true for specific Fahrenheit values:
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Example: Let’s assume \( F = 32 \) (freezing point of water). \[ C = \frac{5}{9}(32 - 32) = \frac{5}{9}(0) = 0 \] The answer checks out since \( 32°F = 0°C \).
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Example: Let’s take \( F = 212 \) (boiling point of water). \[ C = \frac{5}{9}(212 - 32) = \frac{5}{9}(180) = 100 \] The answer checks out since \( 212°F = 100°C \).
Conclusion:
The correct rearranged formula is \( C = \frac{5}{9}(F - 32) \), and it is valid for converting Fahrenheit back to Celsius.
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