At the end of this lesson, students will be able to:
- Solve a two step equation using addition, subtraction, multiplication, and division.
- Solve a two-step equation by combining like terms.
- Solve real-world problems using two-step equations.
Terms introduced in this lesson:
combining like terms
equation in two variables
Teaching Strategies and Tips
Use Example 1 to motivate the process of solving two-step equations:
- Two marbles can be removed from each pan first.
- The first step in solving two-step 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 two-step 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.
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.
Warm-up to Examples 5 and 6 with exercises similar to the following:
Which of the following pairs of expressions are like terms?
x and 5x (Yes.)
x and xy (No.)
x and x2 (No.)
−11 and 11 (Yes.)
In Examples 8 and 9, two-variable equations will result. Students substitute one of the givens for one variable to determine the other.
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.