solve the formula for 1 variable in a literal equation.

Question

The formula F = 9/5 (K-273.15) + 32 converts  temperature from Kelvin K to Fahrenheit F.  Solve the formula for K.  The answer in the book is K = 5/9 (F-32) + 273.15. Please explain, step by step, how they got that answer.

Answer 1

F = 9/5 (K-273.15) + 32

 

You may perform the same operation on both sides of an "=" sign and still have an equation.  Here, we want to isolate "K", so we "undo" (do "-" for "+", do "/" for "*", etc.) what we see as we go along:

 

F = 9/5 (K-273.15) + 32

F - 32 = 9/5 (K-273.15)             [subtract 32 from both sides]

(5/9)(F-32) = K - 273.15             [multiply both sides by (5/9)

(5/9)(F-32) + 273.15 = K           [add 273.15 to both sides]

K = (5/9)(F-32) + 273.15           [you may read equation R-to-L or L-to-R]  

 

 

Answer 2

Hi Janet. Hope all is well.

 

1st: Subtract 32 from both sides. Also a good idea to put parentheses around F - 32 on the left.

2nd: Multiply both sides by 5.

3rd: Divide both sides by 9.

4th: Add 273.15 to both sides.

 

There you go -- you should have the answer!

 

Best wishes.

 

Raffi