To solve the equation \( F = \frac{9}{5}C + 32 \) for \( C \), let's go through it step by step and evaluate the options provided.
1. Start with the original equation:
\[
F = \frac{9}{5}C + 32
\]
2. Subtract 32 from both sides:
\[
F - 32 = \frac{9}{5}C
\]
3. To isolate \( C \), you can multiply both sides by \( \frac{5}{9} \):
\[
C = \frac{5}{9}(F - 32)
\]
Now let's check each option.
A). **First step is to multiply by 9 on each side.**
- FALSE. The first step to isolate C is to subtract 32 from both sides, not multiply by 9.
B). **First step is to add 32 to both sides.**
- FALSE. The first step is to subtract 32 from both sides, not add.
C). **The next step from F - 32 = 9/5 C, could be to multiply both sides by 5.**
- TRUE. You could multiply both sides by 5, but you need to divide by 9 afterwards to isolate C, this step is valid.
D). **The next step from F - 32 = 9/5 C, could be to divide both sides by 5.**
- FALSE. Dividing both sides by 5 would not isolate C, you need to multiply first.
E). **Solution: 5/9F - 32 = C**
- FALSE. The correct solution is \( C = \frac{5}{9}(F - 32) \) or equivalently \( C = \frac{5}{9}F - \frac{160}{9} \) after distributing.
F). **To solve this equation for C, you would have to distribute at some point.**
- TRUE. You would distribute when rearranging to get to the final solution.
**Summary:**
- Options C and F are TRUE.
- Options A, B, D, and E are FALSE.