CHAPTER OUTLINE

4Solving Equations

4.1 Simplifying Expressions and Combining Like Terms4.2 Addition and Subtraction Properties of Equality4.3 Multiplication and Division Properties of Equality4.4 Solving Equations with Multiple Steps

Section 4.1 Homework Questions?

Section

Objectives

4.2 Addition and Subtraction Properties of Equality

1. Definition of a Linear Equation in One Variable2. Addition and Subtraction Properties of Equality

Section 4.2 Addition and Subtraction Properties of Equality

1. Definition of a Linear Equation in One Variable

An equation is a statement that indicates that two quantities are equal.

A solution to an equation is a value of the variable that makes the equation a true statement.

Section 4.2 Addition and Subtraction Properties of Equality

1. Definition of a Linear Equation in One Variable

Note: A linear equation in one variable contains only one variable and the exponent on the variable is 1.

DEFINITION Linear Equation in One Variable

Let a and b be numbers such that a 0. A linear equation in one variable is an equation that can be written in the form ax + b = 0

Avoiding Mistakes

It is important to distinguish between an equation and an expression. An equation has an equal sign, whereas an expression does not. For example:

2x + 4 = 16 equation7x – 9 expression

Example 1 Determining Whether a Number Isa Solution to an Equation

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Determine whether the given number is a solution to the equation.

Section 4.2 You Try

Determine if the provided value is a solution for the given equation.

6 – 3x = 7 (-1) 7x + 4 = 3x + 2 (5)

Section 4.2 Addition and Subtraction Properties of Equality

2. Addition and Subtraction Properties of Equality

Two equations are called equivalent equations if they have the same solution.

PROPERTY Addition and Subtraction Properties of Equality

Section 4.2

To solve an equation, the goal is to isolate the variable on one side of the equation. That is, we want to create an equivalent equation of the form variable = constant.

To accomplish this, we can use the fact that the sum of a number and its opposite is zero.

Example 2 Applying the Addition Property of Equality

Example 3 Applying the Subtraction Property of Equality

Section 4.2 You Try

Solve and check.

a – 9 = -14 x – 5 = 7 x + 6 = 4

PROCEDURE Solving Equations Using the Distributive Property

1. Use the distributive property to remove any grouping symbols.

2. Combine like terms on each side of the equation.

3. Use the Addition or Subtraction Property of Equality to solve the equation.

4. Check your solution.

Example 4 Applying the Addition and Subtraction Properties of Equality

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Section 4.2 You Try

Solve. Remember that you should simplify the expressions on each side of the equation before using the equality property to solve.

x + 3 – 5 = 8 + 2 4(x + 2) - 3x = 17

Section

Objectives

4.2 Addition and Subtraction Properties of Equality

1. Definition of a Linear Equation in One Variable2. Addition and Subtraction Properties of Equality