Page 609 - Basic College Mathematics with Early Integers

Objectives SOLVING EQUATIONS USING ADDITION
8.4 AND MULTIPLICATION PROPERTIES
Solve Equations Using Addition
and Multiplication Properties.
Objective Solving Equations Using Addition
Solve Equations Containing
Parentheses. and Multiplication Properties
Write Numerical Sentences We will now solve equations using more than one property of equality. To solve an
as Equations. equation such as 2x - 6 = 18, we will first get the variable term 2x alone on one
side of the equation.

PRACTICE 1 Example 1 Solve: 2x - 6 = 18
Solve: 5y - 8 = 17
Solution: We start by adding 6 to both sides to get the variable term 2x alone.
2x - 6 = 18
2x - 6 + 6 = 18 + 6 Add 6 to both sides.
2x = 24 Simplify.
To finish solving, we divide both sides by 2.
2x 24
= Divide both sides by 2.
2 2
#
1 x = 12 Simplify.
x = 12

Check:
2x - 6 = 18
21122 - 6 18 Replace x with 12 and simplify.
24 - 6 18
18 18 True
The solution is 12.

Work Practice 1

Make sure you understand which property to use to solve an equation.
Addition Understood multiplication
x + 2 = 10 2x = 10
To undo addition of 2, we subtract 2 from both sides. To undo multiplication of 2, we divide both
x + 2 - 2 = 10 - 2 Use addition sides by 2.
property of 2x 10 Use multiplication
equality. = property of equality.
2 2
x = 8
x = 5
Check: x + 2 = 10
Check: 2x = 10
8 + 2 10
#
2 5 10
10 10 True
10 10 True Copyright 2012 Pearson Education, Inc.
Answer
1. 5

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