# Solving Literal Equations

Literal equations can be tough because less numbers are used. However, you solve these equations exactly the same way, you may just have more variables in your final answer.

I know that in your Math studies, you have come across numerous formulas. Most of these formulas have probably involved geometry!

Have you ever been given a formula, and needed to solve for a variable within the formula? For example, let's take the distance formula. D = rt.

Let's say that you know the distance is 50 ft and the time to travel was 5 minutes. You need to find the rate traveled. In this case, you need to solve for a variable within the formula (rate), and not the standard, (distance).

Yes, I know these problems are always a little more difficult. I'm going to show you a step that will make this problem easier to solve. We are going to be solving literal equations and this means that we will be solving a formula for a given variable.

We are going to use all of the rules that we've learned for solving equations to solve literal equations. You will need to perform "opposite operations" and whatever you do to one side of the equation you must do to the other side of the equation!

Let's look at a couple of examples.

## Example 1: The Distance Formula

Distance Formula:  D = rt

where:

D = distance

r = rate

t = time

• Solve this formula for r. Now we can use our new equation to solve a problem.

• If you need to travel 500 miles in 8 hours, what rate should you maintain? Now let's look at an equation that involves a fraction. Remember to get rid of the fraction first and this will make solving a whole lot easier!

## Example 2 - Literal Equations with Fractions Yes, I know these equations can be tricky. If you are still having trouble, take a look at this video. 