Page 593 - Basic College Mathematics with Early Integers

Objectives 8.2 SOLVING EQUATIONS: THE ADDITION PROPERTY

Determine Whether a Given
Number is a Solution of an
As we mentioned earlier in this book, we have frequently written statements like
Equation.
#
7 + 4 = 11 or Area = length width. Each of these statements is called an equation.
Use the Addition Property of An equation is of the form
Equality to Solve Equations.
expression expression
An equation can be labeled as
equal sign
T
x + 7 = 10
3
c c
left side right side
It is very important to know the difference between an expression and an
equation. An equation contains an equal sign and an expression does not.

Equations Expressions
7x = 6x + 4 7x - 6x + 4
equal no equal signs
signs 3(3y - 5) = 10y y - 1 + 11y - 21

Objective Determining Whether a Number Is a Solution

When an equation contains a variable, finding which values of the variable make an
equation a true statement is called solving an equation for the variable. A solution
of an equation is a value for the variable that makes an equation a true statement.
For example, 2 is a solution of the equation x + 5 = 7 since replacing x with 2
results in the true statement 2 + 5 = 7. Similarly, 3 is not a solution of x + 5 = 7
since replacing x with 3 results in the false statement 3 + 5 = 7.

PRACTICE 1 Example 1 Determine whether 6 is a solution of the equation 41x - 32 = 12.
Determine whether 4 is a
solution of the equation Solution: We replace x with 6 in the equation.
31y - 62 = 6. 41x - 32 = 12
T

416 - 32 12 Replace x with 6.

4132 12
12 12 True
Since 12 = 12 is a true statement, 6 is a solution of the equation.
Work Practice 1
PRACTICE 2 Example 2 Determine whether -1 is a solution of the equation 3y + 1 = 3.

Determine whether -2 is
a solution of the equation Solution:
-4x - 3 = 5. 3y + 1 = 3
31-12 + 1 3
-3 + 1 3 Copyright 2012 Pearson Education, Inc.
-2 3 False
Since -2 = 3 is false, -1 is not a solution of the equation.
Answers
1. no 2. yes Work Practice 2
570