Let's start with the given equation that relates Celsius (C) and Fahrenheit (F):
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
Our goal is to solve for \( C \). We will perform a series of algebraic manipulations to isolate \( C \) on one side of the equation.
1. Subtract 32 from both sides of the equation to remove the constant term on the right side:
[tex]\[
F - 32 = \frac{9}{5}C
\][/tex]
2. Multiply both sides by \( \frac{5}{9} \) to cancel out the coefficient \( \frac{9}{5} \) in front of \( C \):
[tex]\[
\frac{5}{9}(F - 32) = C
\][/tex]
So, the formula that solves for \( C \) in terms of \( F \) is:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
Now let's compare this with the given options to find the correct one:
1. \( c = 4 - \frac{13}{9} \)
- This is not in the form we derived and seems irrelevant to the conversion formula.
2. \( c = \frac{5F}{9} - 22 \)
- This is not correct because it does not correctly account for the \( 32 \) in the original formula and the operations are misplaced.
3. \( C = \frac{3}{5}(F - 3) \)
- This is not correct as the coefficients and constants do not match the derived formula.
4. \( C = \frac{5}{9}(F - 2) \)
- This is close but not correct as the subtraction constant is \( 2 \) instead of \( 32 \).
None of the given options exactly match the derived formula \( C = \frac{5}{9}(F - 32) \).
It appears that the correct formula should be:
[tex]\[ \boxed{C = \frac{5}{9}(F - 32)} \][/tex] and unfortunately, none of the given options matches this formula accurately.
However, if we were to consider a hypothetical situation where there might have been a typographical error in the provided options, the most likely intended correct option among the given choices is:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
We can conclude that the correct conversion formula is:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
