Solving Literal Equations

Sometimes you have a formula and you need to solve for some variable other than the "standard" one. Example: Perimeter of a square P=4s It may be that you need to solve this equation for s, so you can plug in a perimeter and figure out the side length.

This process of solving a formula for a given variable is called "solving literal equations".

One of the dictionary definitions of "literal" is "related to or being comprised of letters“. Variables are sometimes referred to as literals.

So "solving literal equations" may just be another way of saying "taking an equation with lots of variables, and solving for one variable in particular.”

To solve literal equations, you do what you've done all along to solve equations, except that, due to all the variables, you won't necessarily be able to simplify your answers as much as you're used to doing.

Here's how "solving literal equations" works: Suppose you wanted to take the formula for the perimeter of a square and solve it for ‘s’ (or the side length) instead of using it to solve for perimeter. P=4s How can you get the ‘s’ on a side by itself?

P=4s Just as when you were solving linear equations, you want to isolate the variable. So, what do you have to do to get rid of the ‘4’?

P=4s That’s right, you have to divide by ‘4’. You also have to remember to divide both sides by 4.

This new formula allows us to use the perimeter formula to find the length of the sides of a square if we know the perimeter.

Let’s look at another example: 2Q - c = d Multiply both sides by 2.        Subtract ‘c’ from each side.

As you can see, we sometimes must do more that one step in order to isolate the targeted variable. You just need to follow the same steps that you would use to solve any other ‘Multi-Step Equation’.

Work the following on your paper. d = rt Solve for ‘r’

Check your answer. d = rt for ‘r’

Work the following on your paper. P = 2l +2w Solve for ‘w’

Check your answer. P = 2l +2w for ‘w’  

Work the following on your paper. Solve for ‘t’

Check your answer. for ‘t’

Work the following on your paper. mx + 4y = 3t Solve for x

Check your answer. mx + 4y = 3t, solve for x

Work the following on your paper. Solve for b

Check your answer. solve for b

Work the following on your paper. In uniform circular motion, the speed v of a point on the edge of a spinning disk is where r is the radius of the disk and t is the time it takes the point to travel once around the circle. SOLVE the formula for r.

Check your answer. solve for r

Suppose a merry-go-round is spinning once every 3 seconds. If Use the previous slide. Suppose a merry-go-round is spinning once every 3 seconds. If a point on the outside edge has a speed of 12.56 feet per second, what is the radius of the merry-go- round? (use 3.14 for pi)

Check your answer. Suppose a merry-go-round is spinning once every 3 seconds. If a point on the outside edge has a speed of 12.56 feet per second, what is the radius of the merry-go-round? (use 3.14 for pi)

examples around the room. Now you will solve some REAL WORLD examples around the room.