### 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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