### 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 r*^{ 2}, 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 r*^{ 2}
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:
- 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.