To solve the equation \( F = \frac{9}{5}C + 32 \) 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 \( C \): \[ C = \frac{5}{9}(F - 32) \]
Now, let's analyze each statement for its correctness:
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First step is to multiply by 9 on each side.
- False. The first step should involve subtracting 32 from both sides, not multiplying.
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First step is to add 32 to both sides.
- False. Instead, we need to subtract 32 from both sides.
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The next step from \( F - 32 = \frac{9}{5}C \), could be to multiply both sides by 5.
- False. The next logical step would be to multiply both sides by \( \frac{5}{9} \), not just 5.
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The next step from \( F - 32 = \frac{9}{5}C \), could be to divide both sides by 5.
- False. We actually should be multiplying by \( \frac{5}{9} \).
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Solution: \( \frac{5}{9}F - 32 = C \)
- False. The correct solution is \( C = \frac{5}{9}(F - 32) \).
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To solve this equation for C, you would have to distribute at some point.
- True. When finding \( C = \frac{5}{9}(F - 32) \), you can distribute the \( \frac{5}{9} \) if needed.
Therefore, the only true statement is:
- To solve this equation for C, you would have to distribute at some point.