To solve the formula \( F = \frac{9}{5}C + 32 \) for \( C \), let's follow the steps one-by-one:
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Start with the original formula: \[ F = \frac{9}{5}C + 32 \]
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The first step to isolate \( C \) would be to subtract \( 32 \) from both sides: \[ F - 32 = \frac{9}{5}C \]
- So the first statement "First step is to add 32 to both sides." is false. The first step is to subtract \( 32 \), not add.
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The next step involves dealing with the fraction. To isolate \( C \), you can multiply both sides by \( \frac{5}{9} \) (which is the reciprocal of \( \frac{9}{5} \)). Thus: \[ C = \frac{5}{9}(F - 32) \]
Alternatively, you could rearrange it to: \[ C = \frac{5}{9}F - \frac{5}{9} \times 32 \]
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Now looking at the options:
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"The next step from \( F - 32 = \frac{9}{5}C \) could be to multiply both sides by 5" - This is false because you should multiply both sides by \( \frac{5}{9} \), not 5.
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"The next step from \( F - 32 = \frac{9}{5}C \) could be to divide both sides by 5" - This is false for the same reason; you need to multiply by the reciprocal, not divide.
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The exact solution we reached can be rephrased as: \[ C = \frac{5}{9}(F - 32) \]
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If you distribute, it would give a form of \( C = \frac{5}{9}F - \frac{160}{9} \), but that wasn't necessary to state for just solving for \( C \) in the simplest way.
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Hence, the statement "Solution: \( \frac{5}{9}F - 32 = C \)" is false. The correct solution is \( C = \frac{5}{9}(F - 32) \).
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The statement "To solve this equation for \( C\), you would have to distribute at some point." is false in the context of the simplest form of solving for \( C\). You do not have to distribute to find \( C \) in this case; it's optional based on how you express it.
The true answers from the given options based on the explanation above are none of them—everything is found to be false.