Chapter 15: Literal Equations and Formulas

Adapted from Wentworth's Elementary Algebra for MathDoctor.net

15.1 What is a "Literal" Equation?

A literal equation is simply an equation made up mostly or entirely of letters (variables). You aren't looking for a number answer like "x = 5." Instead, you are looking to "solve for" one specific letter in terms of the others.

Example: Distance = Rate × Time (d = rt)

If you know your distance and your rate, but you want to find the time, you need to rearrange the formula to get t by itself.

15.2 The "Do Not Panic" Rule

The rules for moving letters are exactly the same as the rules for moving numbers. If a letter is being multiplied, you divide to move it. If it is being added, you subtract to move it.

Let's solve d = rt for t:

Identify what is happening to t. It is being multiplied by r.
Do the inverse: Divide both sides by r.
d / r = (rt) / r
Result: t = d / r

15.3 Two-Step Literal Equations

Sometimes you have to move a few things. Consider the formula for the perimeter of a rectangle: P = 2l + 2w.

Goal: Solve for w (width).

First, subtract 2l from both sides: P - 2l = 2w
Next, divide the entire other side by 2: (P - 2l) / 2 = w

Chapter 15 Review

Rearrange these formulas for the requested variable:

Solve I = Prt for P. (Simple Interest)
Solve A = bh for b. (Area of a parallelogram)
Solve y = mx + b for x. (Slope-intercept form)
Solve ax + b = c for x.

Chapter 15 Exercises

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Doctor's Recommendation: The Formula Library

Chapter 15 is all about rearranging formulas like Area, Interest, and Distance. The QuickStudy Algebra Reference Guide provides a laminated "cheat sheet" of these common literal equations, giving you a library of real-world formulas to practice your new skills on.

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