Technical Mathematics, Sixth Edition

Chapter 3. Simple Equations and Word Problems

OBJECTIVES When you have completed this chapter, you should be able to Solve simple equations. Check an apparent solution to an equation. Solve simple fractional equations. Solve equations by a graphics calculator and by a calculator that can do symbolic processing. Write an algebraic expression to describe a given verbal statement. Set up and solve simple word problems. Apply the above skills to simple applications in uniform motion, finance, mixtures, and statics.

When two mathematical expressions are set equal to each other, we get an equation. Much of our work in technical mathematics is devoted to solving equations. We start this chapter with the simplest algebraic types, and in later chapters we cover more difficult ones (quadratic equations, exponential equations, trigonometric equations, etc.).

Why is it so important to solve equations? The main reason is that equations are used to describe or model the way certain things happen in the world. Solving an equation often tells us something important that we would not otherwise know. For example, the note produced by a guitar string is not a whim of nature but can be predicted (solved for) when you know the length, the mass, and the tension in the string, and you also know the equation relating the pitch, length, mass, and tension.

Thousands of equations exist that link together various quantities in the physical world—in chemistry, in finance, in manufacturing, and so on—and their ...