Question
Solve this formula for C. Check all answers that are true. (4 points) Responses First step is to multiply by 9 on each side. First step is to multiply by 9 on each side. First step is to add 32 to both sides. First step is to add 32 to both sides. The next step from F - 32 = 9/5 C, could be to multiply both sides by 5 The next step from F - 32 = 9/5 C, could be to multiply both sides by 5 The next step from F - 32 = 9/5 C, could be to divide both sides by 5 The next step from F - 32 = 9/5 C, could be to divide both sides by 5 Solution: 5/9F - 32 = C Solution: 5/9F - 32 = C To solve this equation for C, you would have to distribute at some point.
Answers
GPT-4o mini
Let's analyze the equation \( F - 32 = \frac{9}{5} C \) and solve it for \( C \).
1. **Starting Equation**:
\[
F - 32 = \frac{9}{5} C
\]
2. **First Step Options**:
- **Multiplying by 9** on each side: This isn't a suitable first step since it complicates the equation unnecessarily.
- **Adding 32** to both sides: This is not the first step for solving for \( C \) directly, as we should be isolating \( C \) instead.
3. **Next Steps**:
- **Multiply both sides by 5**:
This can be done to eliminate the fraction, but it's not necessary to get to \( C \) directly. However, it is a valid operation that could be done.
- **Divide both sides by 5**:
This step cannot be done as the \( \frac{9}{5}C \) doesn't allow for direct division by 5 on both sides.
4. **Steps to Solve for \( C \)**:
Let's proceed with solving for \( C \):
\[
F - 32 = \frac{9}{5} C
\]
Multiply both sides by \( \frac{5}{9} \) to isolate \( C \):
\[
\frac{5}{9}(F - 32) = C
\]
This simplifies to:
\[
C = \frac{5}{9}(F - 32)
\]
5. **Final Rearrangement**:
Distributing the \( \frac{5}{9} \):
\[
C = \frac{5}{9}F - \frac{5 \times 32}{9} = \frac{5}{9}F - \frac{160}{9}
\]
While distributing was not necessary for the immediate solution, it provides clarity in the final answer.
Now, let's summarize which statements are true based on this reasoning:
- **The first step is to multiply by 9 on each side.**: False
- **The first step is to add 32 to both sides.**: False
- **The next step from \( F - 32 = \frac{9}{5} C \), could be to multiply both sides by 5.**: True (as a manipulation but not a necessary step to isolate \( C \))
- **The next step from \( F - 32 = \frac{9}{5} C \), could be to divide both sides by 5.**: False
- **Solution: \( \frac{5}{9}F - 32 = C \)**: False (the correct is \( C = \frac{5}{9}F - \frac{160}{9} \) after full distribution)
- **To solve this equation for \( C \), you would have to distribute at some point.**: False (distribution is not necessary to isolate \( C \) but helps clarify)
Conclusions:
- True Statements: The next step from \( F - 32 = \frac{9}{5} C \) could be to multiply both sides by 5.
- False Statements: All other statements.
1. **Starting Equation**:
\[
F - 32 = \frac{9}{5} C
\]
2. **First Step Options**:
- **Multiplying by 9** on each side: This isn't a suitable first step since it complicates the equation unnecessarily.
- **Adding 32** to both sides: This is not the first step for solving for \( C \) directly, as we should be isolating \( C \) instead.
3. **Next Steps**:
- **Multiply both sides by 5**:
This can be done to eliminate the fraction, but it's not necessary to get to \( C \) directly. However, it is a valid operation that could be done.
- **Divide both sides by 5**:
This step cannot be done as the \( \frac{9}{5}C \) doesn't allow for direct division by 5 on both sides.
4. **Steps to Solve for \( C \)**:
Let's proceed with solving for \( C \):
\[
F - 32 = \frac{9}{5} C
\]
Multiply both sides by \( \frac{5}{9} \) to isolate \( C \):
\[
\frac{5}{9}(F - 32) = C
\]
This simplifies to:
\[
C = \frac{5}{9}(F - 32)
\]
5. **Final Rearrangement**:
Distributing the \( \frac{5}{9} \):
\[
C = \frac{5}{9}F - \frac{5 \times 32}{9} = \frac{5}{9}F - \frac{160}{9}
\]
While distributing was not necessary for the immediate solution, it provides clarity in the final answer.
Now, let's summarize which statements are true based on this reasoning:
- **The first step is to multiply by 9 on each side.**: False
- **The first step is to add 32 to both sides.**: False
- **The next step from \( F - 32 = \frac{9}{5} C \), could be to multiply both sides by 5.**: True (as a manipulation but not a necessary step to isolate \( C \))
- **The next step from \( F - 32 = \frac{9}{5} C \), could be to divide both sides by 5.**: False
- **Solution: \( \frac{5}{9}F - 32 = C \)**: False (the correct is \( C = \frac{5}{9}F - \frac{160}{9} \) after full distribution)
- **To solve this equation for \( C \), you would have to distribute at some point.**: False (distribution is not necessary to isolate \( C \) but helps clarify)
Conclusions:
- True Statements: The next step from \( F - 32 = \frac{9}{5} C \) could be to multiply both sides by 5.
- False Statements: All other statements.