Question

The Celsius to Fahrenheit formula: F = 9/5C + 32 ; Solve this formula for C. Check all answers that are true: First step is to multiply by 9 on each side; First step is to add to both sides; The next step from F-32=9/5C, could be to multiply both sides by 5; The next step from F -32= 9/5C, could be divide both sides by 5; Solutions: 5/9F-32=C; To solve this equation for C, you would have to distribute at some point.

Answer 1

Let's solve the equation \( F = \frac{9}{5}C + 32 \) for \( C \) step by step and evaluate the given 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 means the statement "First step is to add to both sides" is false.

3. The next step could involve multiplying both sides by \( \frac{5}{9} \) (not by 5), to isolate \( C \): \[ \frac{5}{9}(F - 32) = C \]

4. We can also write it as: \[ C = \frac{5}{9}(F - 32) \]

   • Thus, we could say \( C = \frac{5}{9}F - \frac{5 \times 32}{9} \), but the equation does not simplify by distributing further for this particular formulation.

Now evaluating the correctness of the statements:

• "First step is to multiply by 9 on each side" - False.
• "First step is to add to both sides" - False (we actually subtract 32).
• "The next step from \( F - 32 = \frac{9}{5}C \), could be to multiply both sides by 5" - False (it would be more useful to multiply both sides by \( \frac{5}{9} \)).
• "The next step from \( F - 32 = \frac{9}{5}C \), could be to divide both sides by 5" - False (you can divide by \( \frac{9}{5} \) but that doesn't directly lead to \( C = \)).
• "Solutions: \( \frac{5}{9}F - 32 = C \)" - False (it should be \( C = \frac{5}{9}(F - 32) \), not \( C = \frac{5}{9}F - 32 \)).
• "To solve this equation for C, you would have to distribute at some point" - False (the equation does not require distribution for solving for C).

Overall, all the statements given are false. The correct form for \( C \) is \( C = \frac{5}{9}(F - 32) \).