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

1 answer

To solve the equation \( F = \frac{9}{5}C + 32 \) 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 \( C \): \[ C = \frac{5}{9}(F - 32) \]

Now, let's analyze each statement for its correctness:

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

    • False. The first step should involve subtracting 32 from both sides, not multiplying.

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

    • False. Instead, 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 logical step would be 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. We actually should be multiplying by \( \frac{5}{9} \).

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

    • False. The correct solution is \( C = \frac{5}{9}(F - 32) \).

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

    • True. When finding \( C = \frac{5}{9}(F - 32) \), you can distribute the \( \frac{5}{9} \) if needed.

Therefore, the only true statement is:

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