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Answer :
To solve the equation [tex]\( C = \frac{5}{9}(F - 32) \)[/tex] for Fahrenheit, [tex]\( F \)[/tex], we can follow these steps:
1. Understand the Equation: The equation [tex]\( C = \frac{5}{9}(F - 32) \)[/tex] describes the relationship between Celsius ([tex]\( C \)[/tex]) and Fahrenheit ([tex]\( F \)[/tex]). Our goal is to express [tex]\( F \)[/tex] in terms of [tex]\( C \)[/tex].
2. Clear the Fraction: To eliminate the fraction, we need to multiply both sides of the equation by 9:
[tex]\[
9C = 5(F - 32)
\][/tex]
3. Distribute the 5: Next, distribute the 5 on the right side of the equation:
[tex]\[
9C = 5F - 160
\][/tex]
4. Isolate the Term with F: To isolate the term involving [tex]\( F \)[/tex], add 160 to both sides:
[tex]\[
9C + 160 = 5F
\][/tex]
5. Solve for F: Finally, divide both sides by 5 to solve for [tex]\( F \)[/tex]:
[tex]\[
F = \frac{9C + 160}{5}
\][/tex]
6. Simplify: Simplifying further, you get:
[tex]\[
F = 1.8C + 32
\][/tex]
This [tex]\( F = 1.8C + 32 \)[/tex] is the formula to convert Celsius to Fahrenheit. You can use it to find the Fahrenheit temperature if you know the Celsius temperature.
1. Understand the Equation: The equation [tex]\( C = \frac{5}{9}(F - 32) \)[/tex] describes the relationship between Celsius ([tex]\( C \)[/tex]) and Fahrenheit ([tex]\( F \)[/tex]). Our goal is to express [tex]\( F \)[/tex] in terms of [tex]\( C \)[/tex].
2. Clear the Fraction: To eliminate the fraction, we need to multiply both sides of the equation by 9:
[tex]\[
9C = 5(F - 32)
\][/tex]
3. Distribute the 5: Next, distribute the 5 on the right side of the equation:
[tex]\[
9C = 5F - 160
\][/tex]
4. Isolate the Term with F: To isolate the term involving [tex]\( F \)[/tex], add 160 to both sides:
[tex]\[
9C + 160 = 5F
\][/tex]
5. Solve for F: Finally, divide both sides by 5 to solve for [tex]\( F \)[/tex]:
[tex]\[
F = \frac{9C + 160}{5}
\][/tex]
6. Simplify: Simplifying further, you get:
[tex]\[
F = 1.8C + 32
\][/tex]
This [tex]\( F = 1.8C + 32 \)[/tex] is the formula to convert Celsius to Fahrenheit. You can use it to find the Fahrenheit temperature if you know the Celsius temperature.
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