To solve the Celsius to Fahrenheit formula \( F = \frac{9}{5}C + 32 \) for \( C \), let's go through the steps.
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Start with the original equation:
\( F = \frac{9}{5}C + 32 \) -
Subtract 32 from both sides:
\( F - 32 = \frac{9}{5}C \) -
Multiply both sides by \( \frac{5}{9} \) to isolate \( C \):
\( C = \frac{5}{9}(F - 32) \)
Which can also be written as:
\( C = \frac{5}{9}F - \frac{160}{9} \)
However, the expression \( C = \frac{5}{9}(F - 32) \) is the more common form to represent it.
Checking the Given Responses
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First step is to multiply by 9 on each side.
False - The first step involves subtracting 32, not multiplying. -
First step is to add 32 to both sides.
False - You need to subtract 32 from both sides, not add. -
The next step from \( F - 32 = \frac{9}{5} C \), could be to multiply both sides by 5.
False - The next step should be to multiply both sides by \( \frac{5}{9} \), not just 5. -
The next step from \( F - 32 = \frac{9}{5}C \), could be to divide both sides by 5.
False - Dividing both sides by 5 does not isolate \( C \). -
Solution: \( \frac{5}{9}F - 32 = C \)
False - This is not correct because it has \( -32 \) on the wrong side. -
To solve this equation for C, you would have to distribute at some point.
False - The distribution is not necessary. You are simply calculating \( \frac{5}{9}(F - 32) \).
Correct Solution
In summary, the correct answer (however not one of the provided options) should be:
Solution: \( C = \frac{5}{9}(F - 32) \)
None of the provided statements are true based on the correct steps needed to solve the equation.