Teaching Notes 3.4: Solving Two-Step Equations with the
Variable on One Side
When students solve two-step equations, they must perform two operations: addition or
subtraction, then multiplication or division.Common errors include performing the operations in
the incorrect order or using incorrect numbers to isolate the variable.- Explain that solving a two-step equation requires students to write two equivalent
equations. Note that an equivalent equation is an equation that has the same solution as the
original equation. - Explain that the first step to solving a two-step equation is to use addition or subtraction
to write an equivalent equation to isolate the variable and its coefficient. You may find it
helpful to review 3.2: ‘‘Solving Equations by Adding or Subtracting.’’ The next step is to use
multiplication or division to write an equivalent equation to solve for the variable. If neces-
sary, review 3.3: ‘‘Solving Equations by Multiplying or Dividing.’’ - Review the information and example on the worksheet. Make sure that your students know
how the numbers that were added, subtracted, multiplied, or divided were used to write the
equivalent equations. Also make certain that they know how these equations were used to
solve the original equation. Depending on the abilities of your students, you may find it nec-
essary to provide more examples. Emphasize the individual steps in solving equations.
EXTRA HELP:
Substitute your answer in the original equation. If the equation is true, your solution is correct.ANSWER KEY:
(1)x= 8 (2)y=− 2 (3)y=− 11 (4)x= 3 (5)x=− 3 (6)y=− 5 (7)y= 18 (8)y=− 20
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(Challenge)Add 13 to both sides to get 1x=28. This is the same asx=28 according to the
multiplication property of one.
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