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

Teaching Notes 3.3: Solving Equations by

Multiplying or Dividing

When students solve equations, they must first isolate the variable on one side of the equation.

A common mistake students make when using multiplication or division to isolate the variable is

to multiply or divide both sides of the equation by an incorrect number.

1. Explain that to solve equations students must first isolate the variable on one side of the
   equation using the multiplication or division property of equality.
   
   
   • The multiplication property of equality states that multiplying both sides of the equation
     by the same nonzero number does not change the value of the variable.
   
   
   • The division property of equality states that dividing both sides of the equation by the
     same nonzero number does not change the value of the variable.
   
   
   
   


2. Review the information and examples on the worksheet with your students. Discuss the
   examples on the worksheet in detail. You may find it helpful to review multiplying and divid-
   ing integers and rational numbers.

EXTRA HELP:

Be sure to check that you have isolated the variable and its coefficient is 1.

ANSWER KEY:

(1)Divide by 6;a=− 7 (2)Multiply by 9;x=− 162 (3)Multiply by−3;x=− 36

(4)Divide by 24;y=−

1

3

(5)Multiply by−1;n=− 100 (6)Multiply by 3;d= 45

(7)Multiply by−

5

3

;x= 100 (8)Multiply by−2;a=− 48 (9)Divide by−13;x=− 2

(10)Multiply by 6;y= 72 (11)Multiply by

4

3

;x= 32 (12)Divide by−2;y= 10

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(Challenge)Both are correct. Dividing both sides by−2 is the same as multiplying both sides

by−

1

2

.

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92 THE ALGEBRA TEACHER’S GUIDE