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### 11.10. Literal Equations and Formulas

A literal equation is one in which some or all of the constants are represented by letters.

## Example 65:

The following is a literal equation:

a(x + b) = b(x + c)

A formula is a literal equation that relates two or more mathematical or physical quantities. These are the equations that describe the workings of the physical world. In Chap. 1 we substituted into formulas. Here we solve formulas or other literal equations for one of its quantities.

#### 11.10.1. Solving Literal Equations and Formulas

When we solve a literal equation or formula, we cannot, of course, get a numerical answer, as we could with a numerical equation. Our object here is to isolate one of the letters on one side of the equal sign. We "solve for" one of the literal quantities.

## Example 66:

Solve for x:

a(x + b) = b(x + c)

Solution: Our goal is to isolate x on one side of the equation. Removing parentheses, we obtain

ax + ab = bx + bc

Subtracting bx and then ab will place all of the x terms on one side of the equation.

axbx = bcab

Factoring to isolate x yields

x(ab) = b(ca)

Dividing by (ab), where ab, gives us

Check: We substitute our answer into our original equation.

We solve literal equations by calculator in the same way we solved numerical equations. Select ...

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