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 x₁.

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.