13. The Celsius to Fahrenheit formula: F=95C+32

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.

Answer 1

Let’s solve the formula $F=\frac{9}{5}C+32$ for $C$ step by step and then evaluate the provided statements.

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. Next, to isolate $C$, multiply both sides by $\frac{5}{9}$: $$C=\frac{5}{9}(F-32)$$

4. This can also be simplified to: $$C=\frac{5}{9}F-\frac{5\times 32}{9}$$

Now, let's evaluate the responses one by one:

1. First step is to multiply by 9 on each side.

   • False: The first step should be to subtract 32 from both sides.

2. First step is to add 32 to both sides.

   • False: We subtract 32 from both sides rather than adding.

3. The next step from $F-32=\frac{9}{5}C$, could be to multiply both sides by 5.

   • False: To isolate $C$, you would multiply by $\frac{5}{9}$ rather than just 5.

4. The next step from $F-32=\frac{9}{5}C$, could be to divide both sides by 5.

   • False: The correct operation would be to multiply by $\frac{5}{9}$.

5. Solution: $\frac{5}{9}F-32=C$

   • False: The correct solution is $C=\frac{5}{9}(F-32)$; the format $\frac{5}{9}F-32$ has the variables in the wrong order.

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

   • True: Distributing is often used when simplifying $\frac{5}{9}(F-32)$, but in this context, it's not necessary if you keep it in factored form.

True Answers

• None of the provided responses are true based on the initial simplification steps and final solution after correctly solving the equation. The only response related to distribution could be considered true in an alternative context, but it was phrased incorrectly as strictly necessary to solve for $C$.