Basic Mathematics for College Students

658 Chapter 8 An Introduction to Algebra

SECTION 8.3

Solving Equations Using Properties of Equality

Objectives

1 Determine whether a number is

a solution.

2 Use the addition property of

equality.

3 Use the subtraction property of

equality.

4 Use the multiplication property

of equality.

5 Use the division property of

equality.

In this section, we introduce four properties of equality that are used to solve

equations.

Determine whether a number is a solution.

An equationis a statement indicating that two expressions are equal. All equations

contain an equal symbol. An example is. The equal symbol separates

the equation into two parts: The expression is the left sideand 15 is the right

side.The letter is the variable(or the unknown). The sides of an equation can be

reversed, so we can write or

• An equation can be true:


• An equation can be false:


• An equation can be neither true nor false. For example, is neither
  true nor false because we don’t know what number represents.
  An equation that contains a variable is made true or false by substituting a number
  for the variable. If we substitute 10 for in , the resulting equation is true:
  . If we substitute 1 for , the resulting equation is false:. A
  number that makes an equation true when substituted for the variable is called a
  solutionand it is said to satisfythe equation. Therefore, 10 is a solution of ,
  and 1 is not.

The Language of Algebra It is important to know the difference between an

equationand an expression. An equation contains an symbol and an

expression does not.



x 5  15

10  5  15 x 1  5  15

x x 5  15

x

x 5  15

2  4  7

6  3  9

x 5  15 15 x 5

x

x 5

x 5  15 

1

Self Check 1

Is 25 a solution of

?

Now TryProblem 19

10 x 35  2 x

EXAMPLE (^1) Is 9 a solution of?
StrategyWe will substitute 9 for each in the equation and evaluate the
expression on the left side and the expression on the right side separately.
WHYIf a true statement results, 9 is a solution of the equation. If we obtain a false
statement, 9 is not a solution.
Solution
Since 26  25 is false, 9 is nota solution of 3 y 1  2 y 7.

26  25

27  1  18  7

Read as “is

possibly equal to.”

3( 9 ) 1 2( 9 ) 7

Evaluate the

expression

on the right

side.

Evaluate the 3 y 1  2 y 7

expression

on the left

side.

y

3 y 1  2 y 7