Let's start with the formula for converting Celsius to Fahrenheit:
\[ F = \frac{9}{5}C + 32 \]
We want to solve for \( C \). We'll go through the steps to rearrange the equation:
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Subtract 32 from both sides: \[ F - 32 = \frac{9}{5}C \]
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Now, multiply both sides by \( \frac{5}{9} \) to solve for \( C \): \[ C = \frac{5}{9}(F - 32) \]
This can also be written as: \[ C = \frac{5}{9}F - \frac{5 \times 32}{9} \]
Now, let’s look at the statements and identify the true ones based on our steps:
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First step is to multiply by 9 on each side.
False. The first step is to subtract 32 from both sides. -
First step is to add 32 to both sides.
False. We need to subtract 32 from both sides. -
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 \(\frac{5}{9}\) to isolate \( C \). -
The next step from F - 32 = \(\frac{9}{5}C\), could be to divide both sides by 5.
False. We should not divide both sides by 5; instead, we multiply by \(\frac{5}{9}\). -
Solution: \(\frac{5}{9}F - 32 = C\)
False. This expression is incorrect as it does not correctly represent \( C \). The correct representation is \( C = \frac{5}{9}(F - 32) \). -
To solve this equation for C, you would have to distribute at some point.
True. After multiplying by \(\frac{5}{9}\), you would distribute when calculating \( C \) if you were rearranging that expression further.
So, the only true statement from the options given is:
To solve this equation for C, you would have to distribute at some point.