Question

The Celsius to Fahrenheit formula: F=95C+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

Let's start with the formula for converting Celsius to Fahrenheit:

\[ F = \frac{9}{5}C + 32 \]

We want to solve for \( C \). We'll go through the steps to rearrange the equation:

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

2. Now, multiply both sides by \( \frac{5}{9} \) to solve for \( C \):
\[
C = \frac{5}{9}(F - 32)
\]

This can also be written as:
\[
C = \frac{5}{9}F - \frac{5 \times 32}{9}
\]

Now, let’s look at the statements and identify the true ones based on our steps:

1. **First step is to multiply by 9 on each side.**
**False.** The first step is to subtract 32 from both sides.

2. **First step is to add 32 to both sides.**
**False.** We need 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 next step should be to multiply both sides by \(\frac{5}{9}\) to isolate \( C \).

4. **The next step from F - 32 = \(\frac{9}{5}C\), could be to divide both sides by 5.**
**False.** We should not divide both sides by 5; instead, we multiply by \(\frac{5}{9}\).

5. **Solution: \(\frac{5}{9}F - 32 = C\)**
**False.** This expression is incorrect as it does not correctly represent \( C \). The correct representation is \( C = \frac{5}{9}(F - 32) \).

6. **To solve this equation for C, you would have to distribute at some point.**
**True.** After multiplying by \(\frac{5}{9}\), you would distribute when calculating \( C \) if you were rearranging that expression further.

So, the only **true** statement from the options given is:
**To solve this equation for C, you would have to distribute at some point.**