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

Solve this formula for C. Check all answers that are true.
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 \( C \), 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 \( C \):
    \( C = \frac{5}{9}(F - 32) \)

  3. Distributing gives:
    \( C = \frac{5}{9}F - \frac{5}{9} \cdot 32 \)

Now let's evaluate the statements:

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

  • False. The first step is to subtract 32, not to multiply by 9.

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

  • False. The first step is to subtract 32 from both sides.

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

  • False. To isolate \( C \), we need to multiply by \( \frac{5}{9} \), not 5.

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

  • False. While dividing by 5 does happen eventually when isolating \( C \), the correct next step is to use \( \frac{5}{9} \) to isolate \( C \).

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. After multiplying by \( \frac{5}{9} \), you would distribute when simplifying the equation.

In summary, the only true statement is F.

there's multiple correct answers so please choose them

Let's carefully evaluate each option based on solving the equation \( F = \frac{9}{5}C + 32 \) for \( C \):

  1. First, rewrite the equation: \( F - 32 = \frac{9}{5}C \).

Now, let's assess each of the statements:

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

  • False. The first step is not to multiply by 9; we actually subtract 32 first.

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

  • False. The first step is to subtract 32 from both sides, not add.

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

  • True. While it's not the ideal step, you could multiply both sides by 5 to get rid of the fraction. However, you would then need to correctly handle the equation subsequently, as multiplying by 5 alone won't isolate \( C \).

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

  • False. This does not isolate \( C \)—it isn't a valid step in solving for \( C \) directly.

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

  • False. The correct solution should be of the form \( C = \frac{5}{9}(F - 32) \).

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

  • True. If you use the form \( C = \frac{5}{9}(F - 32) \), you would eventually distribute the \( \frac{5}{9} \).

Correct Answers:

  • C (you could multiply both sides by 5 to eliminate the fraction, though not the best immediate step)
  • F (you would have to distribute at some point)

Thus, the correct choices are C and F.

this is it?

Let’s re-evaluate the statements carefully again to ensure we capture all applicable correct answers regarding solving the equation \( F = \frac{9}{5}C + 32 \) for \( C \).

  1. Rearrangement: Start with \( F = \frac{9}{5}C + 32 \):

    • Move 32 to the other side:
      \( F - 32 = \frac{9}{5}C \)

  2. Isolate \( C \):

    • Multiply both sides by \( \frac{5}{9} \):
      \( C = \frac{5}{9}(F - 32) \)

Now, let’s go through each statement again:

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

  • False. The first step is to subtract 32, not multiply.

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

  • False. The correct first step is to subtract 32 from both sides.

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

  • True. You could multiply both sides by 5, but then you still need to divide by 9.

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

  • False. Simply dividing both sides by 5 wouldn't isolate \( C \) effectively since you would still have the fraction.

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

  • False. The correct solution should be \( C = \frac{5}{9}(F - 32) \), not the form stated.

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

  • True. When arriving at \( C = \frac{5}{9}(F - 32) \), distributing is part of simplifying the expression.

Final Valid Answers:

  • C (true)
  • F (true)

Thus, the correct answers to select are indeed C and F. Thank you for your patience, and I hope this clears up any confusion!