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

Teaching Notes 3.2: Solving Equations by Adding

or Subtracting

When solving equations, students must understand that the most important step is to isolate the

variable on one side of the equation. This is done by using inverse operations such as addition

and subtraction. A common mistake in solving one-step equations is adding or subtracting the

wrong number from both sides of the equation.

1. Explain to your students that in order to solve an equation, they must isolate the variable on
   one side of the equation.


2. Review the information and examples on the worksheet with your students. Discuss the addi-
   tion property of equality and the subtraction property of equality.
   
   
   • The addition property of equality states that adding the same number to both sides of the
     equation does not change the value of the variable.
   
   
   • The subtraction property of equality states that subtracting the same number from both
     sides of the equation does not change the value of the variable.
     To help students find what numbers to add or subtract, offer examples such as− 5 +what
     number=0, 3−what number=0, and 6+what number=0. (The answers are 5, 3, and
     −6.) Emphasize that to solve these problems, students are adding the same number to or sub-
     tracting the same number from both sides of the equation. Note that in the second example
     students must use the definition of subtraction to rewrite the problem as addition. Depend-
     ing on the abilities of your students, you may wishto review adding and subtracting integers
   
   
   
   

andRationalNumbers

EXTRA HELP:

You must add or subtract the same number to or from both sides of the equation.

ANSWER KEY:

(1)Subtract 6;x= 9 (2)Add 7;x= 27 (3)Subtract 4;y= 9 (4)Add 32;z= 28

(5)Add 3;x=− 5 (6)Add 6;n=− 3 (7)Add 4;s= 0 (8)Add

3

5

;n= 1

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(Challenge)Mike used a shortcut and his method is correct, but he did not show all of his work.

He added−3 and 2 mentally to get−1. Then he added 1 to both sides to getx=−9.

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90 THE ALGEBRA TEACHER’S GUIDE