To solve the equation \( F = \frac{9}{5}C + 32 \) for \( C \), let's go through the steps properly and verify the responses provided.
Original Equation
\[ F = \frac{9}{5}C + 32 \]
Step 1: Subtract 32 from both sides
To isolate the term with \( C \), we first subtract 32 from both sides: \[ F - 32 = \frac{9}{5}C \]
This checks out with the choice:
- First step is to add 32 to both sides. (False)
Step 2: Multiply both sides by \( \frac{5}{9} \)
To solve for \( C \), multiply both sides by \( \frac{5}{9} \): \[ C = \frac{5}{9}(F - 32) \]
Final Step: Rewrite the equation
We can also rearrange it to: \[ C = \frac{5}{9}F - \frac{5 \times 32}{9} \] However, this isn't necessary for the answer to be correct.
Solutions and Verification of Responses
The following responses can be assessed based on our solution process:
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First step is to multiply by 9 on each side. - (False)
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First step is to add 32 to both sides. - (False)
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The next step from F - 32 = 9/5 C, could be to multiply both sides by 5. - (False)
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The next step from F - 32 = 9/5 C, could be to divide both sides by 5. - (False)
(The next logical step was to multiply by \( \frac{5}{9} \), not divide or multiply by 5.)
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Solution: 5/9F - 32 = C. - (False)
(The correct form from our derivation would be \( C = \frac{5}{9}(F - 32) \), which when expanded gives you \( C = \frac{5}{9}F - \frac{160}{9} \)).
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To solve this equation for C, you would have to distribute at some point. - (True)
(If we expand \( C = \frac{5}{9}(F - 32) \), we indeed distribute \( \frac{5}{9} \) over both terms.)
Summary of True/False
- False responses: 1, 2, 3, 4, 5
- True response: 6
Based on the solution and analysis, the only true statement is:
- To solve this equation for C, you would have to distribute at some point.