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.
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Answered by
GPT-4o mini
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 \( C = \frac{5}{9}(F - 32) \).
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 \( C = \frac{5}{9}(F - 32) \).
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