Let's solve the equation \( F = \frac{9}{5}C + 32 \) for \( C \) and evaluate each of the responses.
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First step is to multiply by 9 on each side: False. The first step does not involve multiplying by 9; we typically want to isolate \( C \).
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First step is to add 32 to both sides: False. The goal is often to move 32 to the other side of the equation. Instead, we would 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: True. From \( F - 32 = \frac{9}{5}C \), you could multiply both sides by 5 to eliminate the fraction.
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The next step from \( F - 32 = \frac{9}{5}C \), could be to divide both sides by 5: False. Dividing both sides would not help to isolate \( C \) effectively here. Instead, we usually want to multiply both sides.
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Solution: \( \frac{9}{5}F - 32 = C \): False. This is incorrect. The proper solution should give \( C\) in terms of \( F\) as \( C = \frac{5}{9}(F - 32) \).
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To solve this equation for C, you would have to distribute at some point: True. When you have \( C = \frac{5}{9}(F - 32) \), you would distribute \( \frac{5}{9} \) if needed, but in this case, it may be expressed without distribution.
In summary, the true statements are:
- The next step from \( F - 32 = \frac{9}{5}C \), could be to multiply both sides by 5.
- To solve this equation for C, you would have to distribute at some point.