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

Teaching Notes 3.6: Solving Equations with Variables

on Both Sides

The strategy for solving an equation with variables on both sides is to add or subtract a variable

expression to or from both sides of the equation so that the variable is on only one side of the

equation. Common errors include selecting an incorrect variable expression and not simplifying

the problem first.

1. Explain that variable expressions can be added or subtracted on both sides of an equation. If
   necessary, remind students that a variable expression is a variable and its numerical coeffi-
   cient. For example, 2x,

1

3

x,and− 4 xare variable expressions.

2. Explain that before students can add a variable expression to or subtract a variable expres-
   sion from both sides of an equation, each side of the equation must be in simplest form. An
   equation in simplest form has no parentheses and like terms are combined. You may wish to
   review 3.5: ‘‘Solving Equations Using the Distributive Property.’’


3. Provide this example: 3x+ 12 = 7 x. Note that it is already in simplest form. Ask your stu-
   dents what variable expression they would subtract from each side. They should subtract 3x
   to get 12= 4 x. Dividing both sides of the equation by 4 results in the solutionx=3.


4. Review the information and example on the worksheet with your students. Point out that
   the example problem may be solved in either of two ways. Each requires the same number of
   steps.

EXTRA HELP:

Be sure all parentheses are eliminated and all similar terms are combined before adding or

subtracting the variable expressions to or from both sides of the equation.

ANSWER KEY:

(1)y= 4 (2)x=− 17 (3)y=− 13 (4)x=− 19 (5)y=− 30 (6)x=− 7 (7)x= 15 (8)y= 13

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(Challenge)Meg did not simplify before she subtracted 3x. The correct equivalent equation is

------------------------------------------------------------------------------------------^3 x+^6 =^4 x. She should have subtracted 3xfrom both sides to getx=6.

98 THE ALGEBRA TEACHER’S GUIDE