Solving Literal Equations - Problem 2 7,641 views

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

When solving literal equations that involve solving for a variable when there is more than one variable, use the same rules you would with any single variable equation. Just like you can add 3 to both sides of an equation, you can add/subtract/multiply/divide a variable to both sides of the equation. Remember that the goal is to "undo" what is being done to the variable that you must solve for. Use inverse operations to eliminate all other variables and numbers on the same side of the equal sign.

This exact problem is probably another one that your math teacher is going to assign to you and if it's not in your homework, there's a good chance it's going to be on your test guys. This is a really common problem that has to do with solving equations that have lots of letters. The formula to convert from Celsius to Fahrenheit is F is equal to 9/5C plus 32. What formula would you use to convert from Fahrenheit to Celsius? So what I want to do is take this formula and instead of having F all by itself, I want to get C all by itself. I'm just going to rewrite it down here so I have more space 9/5C plus 32.

To get C all by itself I need to undo these other two operations. First I'm going to undo the plus 32 by subtracting 32 from both sides and now I have F-32 equals 9/5 times C. Well right now C is being multiplied by a fraction and the opposite of multiplying by a fraction, the way to undo that would be to multiply by that fraction's reciprocal. I'm going to multiply by 5/9. Please don't forget these parentheses.

Everything on this left hand side of the equation is going to get multiplied by that 5/9. A lot of students make the error of just writing 5/9F take away 32, they forget that 5/9 is also multiplied by that 32. So these cancel out and I'm left with now 5/9F, 5/9 times my degrees Fahrenheit take away 5/9 times 32, we'll see what that is in a second on my calculator, and I'm going to get my answer for C. So on your calculator the way to do that product 5/9 times -32, would be to first do 5 divided by 9 then whatever that answer is you're going to multiply by 32 and sick a negative sign out front. I got 17.77 repeating so I'm going to write 17.77 repeating like that. This is my final answer.

If I were given a degree in Fahrenheit and I wanted to turn it into a degree in Celsius, first I would multiply by 5/9 and then take away 17.7 repeating. This, as you guys can see, is really, really useful any time you travel outside your home country like here in the United States we use Fahrenheit but I know in other places around the world they use Celsius. So this is the kind of calculation you're going to want to keep handy any time you travel.