3.1. Solving a Simple Equation

Let's start this chapter by learning how to solve a simple equation. Then we will be able to apply those skills to the verbal problems that come a bit later.

3.1.1. Equations

An equation has two sides and an equal sign.

A conditional equation is one whose sides are equal only for certain values of the variable.

Example 1:

The equation

x − 5 = 0

is a conditional equation because the sides are equal only when x = 5. When we say "equation," we will mean "conditional equation." An equation that is true for any value of the variable, such as x(x + 2) = x2 +2x, is called an identity. The symbol ≡ is often used for identities. We would write x(x + 2) ≡ x2 + 2x.

3.1.2. First-Degree Equations

In this chapter we will limit ourselves to solving first-degree equations. Recall that a first-degree term is one in which the variable is raised to the power 1 (which is not written), and that a first-degree equation is one in which no term is higher than first degree. A first-degree equation is also called a linear equation. We also limit ourselves here to equations having just one variable.

Example 2:

The equation

3(x + 4) = 2(x − 5)

is a first-degree equation in one variable, the type we will cover in this chapter.

3.1.3. The Solution of an Equation

The value of the variable that makes the sides of an equation equal to each other is called a solution to that ...

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