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

Solve this formula for C. Check ALL!!! Answers that are TRUE!!.

options:

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.

1 answer

Let's go through the process of solving the Celsius to Fahrenheit formula \( F = \frac{9}{5}C + 32 \) for \( C \).

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

  2. First step: Subtract 32 from both sides to isolate the term involving \( C \): \[ F - 32 = \frac{9}{5}C \]

  3. Now we have: \[ F - 32 = \frac{9}{5}C \]

  4. Next step: To eliminate the fraction, we can multiply both sides by \( \frac{5}{9} \): \[ \frac{5}{9}(F - 32) = C \]

Now let's check the options provided:

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

    • FALSE: Dividing both sides by 5 would not correctly isolate \( C \); it should involve multiplying by \( \frac{5}{9} \).
  • E) Solution: \( \frac{5}{9} F - 32 = C \).

    • FALSE: The correct solution is \( C = \frac{5}{9}(F - 32) \), not \( \frac{5}{9} F - 32 \).
  • F) To solve this equation for C, you would have to distribute at some point.

    • FALSE: You do not need to distribute anything when isolating \( C \) since \( F - 32 \) is already grouped.

In summary, all options are FALSE.