# 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.

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