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# Literal Equations

By the end of this section, you should be able to solve the following problems.

1. Solve for the indicated variable.

5y − 3x = −2 for x

2. Solve for the given variable.

3. Solve for the indicated variable.

## 2 Concepts

In previous sections, you studied how to solve an equation for a particular

number. In this section we use the exact same reasoning to solve for a

particular letter. Below is an example.

**2.1 Example**

Solve the following equation for x_{1}.

We don’t like negative signs in our denominators, so
change the denominator

to a positive and change all the signs in the numerator to get.

In our next example we also solve for a single letter.

**2.2 Example**

Solve the following equation for x.

Tx + by = r

Our next example is the familiar perimeter equation.

**2.3 Example**

Solve for l in the following equation.

When dividing both sides by a letter or number, make sure
to divide

the entire expression on both sides by that letter or number. For example,

when solving for R in the expression below we divide the entire

expression on both sides by h

## 3 Exercises

1. Solve for the indicated variable.

5y − 3x = −2 ; for x

2. Solve for C.

3. Solve for the indicated variable.

## 4 Solutions

1. Solve for the indicated variable.

2. Solve for C.

3. Solve for the indicated variable.