3.2: TwoStep Equations
Learning Objectives
At the end of this lesson, students will be able to:
 Solve a two step equation using addition, subtraction, multiplication, and division.
 Solve a twostep equation by combining like terms.
 Solve realworld problems using twostep equations.
Vocabulary
Terms introduced in this lesson:
 twostep equations
 like terms
 combining like terms
 unknown
 equation in two variables
Teaching Strategies and Tips
Use Example 1 to motivate the process of solving twostep equations:
 Two marbles can be removed from each pan first.
 The first step in solving twostep equations is to move the constant away from the variable term.
 Whereas it was not possible before, the marbles can now be divided into three groups.
 The second step in solving twostep equations is to isolate the variable by dividing by its coefficient.
 It is a small jump for students to write an algebraic expression based on the equality implied by the pans and solve it in an analogous way.
To keep the pans in equilibrium, Example 1 also teaches that, “what is done to one side must be done to the other side”.
Because the solution to Example 2 is negative, the balance strategy of Example 1 will not apply. Use a similar problem in which the solution is positive to demonstrate the balance strategy for variables buried in parentheses.
Example.
Six bags each containing the same unknown number of blue marbles and
Solution. The unknown quantity is the number of blue marbles in each bag and is denoted by
This is an example of an equation where
The first approach is easier since
General Tip: The first step in solving equations with variables buried in parentheses depends on:
 Whether the constant is evenly divisible by the coefficient. See Example 2.
 Whether fractions are present. See Examples 3 and 4.
Warmup to Examples 5 and 6 with exercises similar to the following:
Which of the following pairs of expressions are like terms?

x and5x (Yes.) 
x andxy (No.) 
x andx2 (No.) 
−11 and11 (Yes.)
In Examples 8 and 9, twovariable equations will result. Students substitute one of the givens for one variable to determine the other.
Error Troubleshooting
Watch for the switch from Example 9(ii) to 9(iii), from Celsius to Fahrenheit.
Review Question 1c. Remind students to distribute the negative to both terms in the parentheses.
Review Question 1g. Hint: Write the
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