Chapter 4 - Equations

Equations express relationships among quantities. They are statements of mathematical facts or of physical laws.

In geometry, for example, we can write down the equation A = π r², which relates the area A of a circle to its radius r. This equation is a mathematical fact. In physics we can write down the equation F = m a, which relates the amount of acceleration a that an object with mass m undergoes when a force F is applied to it. This equation is a law of nature called Newton’s law of motion.

If we are given a value for the radius of a circle then we can substitute it into the equation A = π r² and immediately get out the area of the circle. However if we are given the area and want to find the radius then we have to solve the equation for the radius.

This chapter and much of this book is concerned with solving equations. This chapter contains the following sections:

section 4.1 - In this section we introduce equations and their solutions. Then we talk about two types of equations that are easy to solve:
- equations in which the unknown appears just once, and
- equations of the factored form a · b = 0.
section 4.2 - In this section we show how to solve the simplest equations in which the unknown appears more than once, namely linear equations. Specifically we talk about these techniques:
Then we present a flowchart for solving equations. In later chapters we will learn more specialized procedures for solving more specialized equation types and will add to this flowchart.