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


Solve this formula for C. Check all answers that are true.

(4 points)

A. First step is to multiply by 9 on each side.
B. First step is to add 32 to both sides.
C. The next step from F - 32 = 9/5 C, could be to multiply both sides by 5
D. The next step from F - 32 = 9/5 C, could be to divide both sides by 5
E. Solution: 5/9F - 32 = C
F. To solve this equation for C, you would have to distribute at some point.

5 answers

To solve the equation \( F = \frac{9}{5}C + 32 \) for \( C \), let's follow the correct steps:

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

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

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

This simplification results in: \[ C = \frac{5}{9}F - \frac{160}{9} \]

So, let's evaluate the options based on this process:

A. First step is to multiply by 9 on each side. - False (The first step is to subtract 32.)

B. First step is to add 32 to both sides. - False (It should be subtracting 32.)

C. 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 by \( \frac{5}{9} \).)

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

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

F. To solve this equation for C, you would have to distribute at some point. - True (In the final step, distribution would occur when expressing \( C \) as \( C = \frac{5}{9}F - \frac{160}{9} \).)

Thus, the only true statement is:

  • F. To solve this equation for C, you would have to distribute at some point.
SOLVE FOR CELSIUS.. PLEASE

To solve for Celsius \( C \) in the Celsius to Fahrenheit conversion formula \( F = \frac{9}{5}C + 32 \), let's go through the steps clearly:

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

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

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

  4. To express it more clearly, you can also distribute: \[ C = \frac{5}{9}F - \frac{5 \times 32}{9} \] Which simplifies to: \[ C = \frac{5}{9}F - \frac{160}{9} \]

So, the final formula to convert Fahrenheit \( F \) to Celsius \( C \) is: \[ C = \frac{5}{9}(F - 32) \]

This formula allows you to calculate Celsius based on a given Fahrenheit temperature. If you have a specific Fahrenheit temperature in mind, feel free to provide it, and I can help you calculate the Celsius equivalent!

There is not an option to subtract..

I apologize for the confusion earlier. Let's clarify how to rearrange the formula \( F = \frac{9}{5}C + 32 \) to solve for \( C \), avoiding any steps that involve subtraction explicitly since you mentioned that's not allowed.

Here are the steps to isolate \( C \):

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

  2. To eliminate \( 32 \) from the right side, we can manipulate the equation in a way that leads us to isolate \( C \). While you might not want to explicitly subtract, we can rearrange it conceptually: \[ F - 32 = \frac{9}{5}C \]

  3. Now, let's multiply both sides by \( \frac{5}{9} \) to isolate \( C \): \[ C = \frac{5}{9}(F - 32) \]

This step is effectively adjusting the equation so that \( C \) is on one side. The final solution is: \[ C = \frac{5}{9}(F - 32) \]

If you want to express it in another way to avoid talking about subtraction, you could think of it as finding \( C \) based on \( F \) and the known linear transformation involved.

Please let me know if you need further clarification or a different approach!