The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 3.5: Solving Equations Using the

Distributive Property

When solving an equation that contains parentheses,students must use the distributive property

to eliminate the parentheses and isolate the variable. Many students have trouble applying the

distributive property and they are then unable to solve the equation correctly.

1. Discuss the distributive property with your students.a(b+c)=ab+acanda(b−c)=
   ab−ac. Depending on the abilities of your students, you may find it helpful to provide
   additional examples, such as 3(x+5), which is equal to 3(x)+3(5)= 3 x+15, and
   −5(x−2), which is equal to−5(x)+(−5)(−2)=− 5 x+10.


2. Provide the following example: 2(x+5)=20. Instruct your students to first rewrite the
   equation using the distributive property. 2x+ 10 =20. Next have students isolate the
   variable by subtracting 10 from both sides and dividing by 2. The answer isx=5.


3. Review the information and examples on the worksheet with your students. Explain that in
   some equations they may need to combine similar terms. If necessary, explain that similar
   terms are terms that have the same variable or variables raised to the same power, such asx
   and 6x. Remind your students to check their work. (Note:The examples on the worksheet do
   not include the checks.)

EXTRA HELP:

The number outside parentheses must be multiplied by each term inside the parentheses.

ANSWER KEY:

(1)x= 25 (2)x=− 1 (3)x= 5 (4)x=− 12 (5)x= 2 (6)x= 2

2

3

(7)x=− 10 (8)x=

1

3

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(Challenge)The error was in the first step and caused subsequent errors throughout the problem.

The correct steps are− 3 x− 36 =15;− 3 x=51;x=−17.

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96 THE ALGEBRA TEACHER’S GUIDE