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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 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.

3 answers

Let's solve the equation \( F = \frac{9}{5}C + 32 \) for \( C \) step-by-step and check the statements.

  1. Start with the original equation: \[ F = \frac{9}{5}C + 32 \]

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

    • This aligns with the statement: "First step is to add 32 to both sides." (This statement is FALSE; we actually subtract 32.)

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

    • Here, we are effectively multiplying both sides by \( \frac{5}{9} \).

  4. Distributing: \[ C = \frac{5}{9}F - \frac{5}{9} \times 32 \]

    • This shows that we do indeed distribute at some point.

Now, let's evaluate the provided options:

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

  2. First step is to add 32 to both sides. (FALSE)

  3. The next step from \( F - 32 = \frac{9}{5}C \), could be to multiply both sides by 5. (FALSE) (You would multiply by \( \frac{5}{9} \), not 5.)

  4. The next step from \( F - 32 = \frac{9}{5}C \), could be to divide both sides by 5. (FALSE) (You divide by \( \frac{9}{5} \), which is the same as multiplying by \( \frac{5}{9} \).)

  5. Solution: \( \frac{5}{9}F - 32 = C \). (FALSE) (The correct solution includes subtracting \( \frac{5 \times 32}{9} \).)

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

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

its multiple choice

Thank you for clarifying that this is a multiple-choice question. Let's evaluate the statements based on our previous analysis.

Here are the correct responses to check:

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

    • (FALSE)

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

    • (FALSE)

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

    • (FALSE)

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

    • (FALSE)

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

    • (FALSE) (The correct form should be \( C = \frac{5}{9}(F - 32) \))

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

    • (TRUE)

So, in summary, the only TRUE statement is:

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

This is the correct answer to select in a multiple-choice format.