Question

The Celsius to Fahrenheit formula: F=9/5 C + 32

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 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 divide both sides by 5


Solution: 5/9F - 32 = C

To solve this equation for C, you would have to distribute at some point.

Answer 1

To solve the Celsius to Fahrenheit formula \( F = \frac{9}{5} C + 32 \) for \( C \), we can follow these steps:

1. **Subtract 32 from both sides**:
\[
F - 32 = \frac{9}{5} C
\]

2. **Multiply both sides by \( \frac{5}{9} \)** to isolate \( C \):
\[
C = \frac{5}{9} (F - 32)
\]

3. **Distribute \( \frac{5}{9} \)**:
\[
C = \frac{5}{9}F - \frac{5}{9} \times 32
\]

So, the final solution is:
\[
C = \frac{5}{9}F - \frac{160}{9}
\]

### Evaluating the Responses:

1. **First step is to multiply by 9 on each side.**
- **False.** The first step is to subtract 32 from both sides, not to multiply.

2. **First step is to add 32 to both sides.**
- **False.** The correct first step is to subtract 32 from both sides.

3. **The next step from \( F - 32 = \frac{9}{5} C \) could be to multiply both sides by 5.**
- **False.** The correct step is to multiply both sides by \( \frac{5}{9} \), not just 5.

4. **The next step from \( F - 32 = \frac{9}{5} C \) could be to divide both sides by 5.**
- **False.** Dividing by 5 wouldn't correctly isolate \( C \) since it is currently multiplied by \( \frac{9}{5} \).

5. **Solution: \( \frac{5}{9}F - 32 = C \)**
- **False.** The correct solution should distribute the \( \frac{5}{9} \) to both terms: \( C = \frac{5}{9}F - \frac{160}{9} \).

6. **To solve this equation for \( C \), you would have to distribute at some point.**
- **True.** Distributing the \( \frac{5}{9} \) is necessary to arrive at the final equation in terms of \( C \).

### Summary of True/False Statements:

- 1: **False**
- 2: **False**
- 3: **False**
- 4: **False**
- 5: **False**
- 6: **True**