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Answer :
We start with the formula that converts Celsius to Fahrenheit:
[tex]$$
F = \frac{9}{5}C + 32.
$$[/tex]
Our goal is to solve for [tex]$C$[/tex] in terms of [tex]$F$[/tex]. Here are the steps:
1. Subtract 32 from both sides:
Subtract [tex]$32$[/tex] from both sides of the equation:
[tex]$$
F - 32 = \frac{9}{5}C.
$$[/tex]
2. Multiply by the reciprocal of [tex]$\frac{9}{5}$[/tex]:
To isolate [tex]$C$[/tex], we multiply both sides by the reciprocal of [tex]$\frac{9}{5}$[/tex], which is [tex]$\frac{5}{9}$[/tex]:
[tex]$$
C = \frac{5}{9}(F - 32).
$$[/tex]
3. Express as a single fraction (optional):
Distribute [tex]$\frac{5}{9}$[/tex]:
[tex]$$
C = \frac{5}{9}F - \frac{5 \times 32}{9} = \frac{5}{9}F - \frac{160}{9}.
$$[/tex]
Thus, the formula that converts degrees Fahrenheit to degrees Celsius is:
[tex]$$
C = \frac{5}{9}(F - 32) \quad \text{or equivalently} \quad C = \frac{5F}{9} - \frac{160}{9}.
$$[/tex]
[tex]$$
F = \frac{9}{5}C + 32.
$$[/tex]
Our goal is to solve for [tex]$C$[/tex] in terms of [tex]$F$[/tex]. Here are the steps:
1. Subtract 32 from both sides:
Subtract [tex]$32$[/tex] from both sides of the equation:
[tex]$$
F - 32 = \frac{9}{5}C.
$$[/tex]
2. Multiply by the reciprocal of [tex]$\frac{9}{5}$[/tex]:
To isolate [tex]$C$[/tex], we multiply both sides by the reciprocal of [tex]$\frac{9}{5}$[/tex], which is [tex]$\frac{5}{9}$[/tex]:
[tex]$$
C = \frac{5}{9}(F - 32).
$$[/tex]
3. Express as a single fraction (optional):
Distribute [tex]$\frac{5}{9}$[/tex]:
[tex]$$
C = \frac{5}{9}F - \frac{5 \times 32}{9} = \frac{5}{9}F - \frac{160}{9}.
$$[/tex]
Thus, the formula that converts degrees Fahrenheit to degrees Celsius is:
[tex]$$
C = \frac{5}{9}(F - 32) \quad \text{or equivalently} \quad C = \frac{5F}{9} - \frac{160}{9}.
$$[/tex]
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