Some Potential Dangers when Solving Equations

Examples, videos, and solutions to help Algebra I students learn the process of solving equations.

New York State Common Core Math Algebra I, Module 1, Lesson 13

Worksheets for Algebra I, Module 1, Lesson 13 (pdf)

Student Outcomes
Students learn “if-then” moves using the properties of equality to solve equations. Students also explore moves that may result in an equation having more solutions than the original equation.

Lesson 13 Summary
Assuming that there is a solution to an equation, applying the distribution, commutative, and associative properties and the properties of equality to equations will not change the solution set.

Feel free to try doing other operations to both sides of an equation, but be aware that the new solution set you get contains possible CANDIDATES for solutions. You have to plug each one into the original equation to see if they really are solutions to your original equation.

Exercise 1
a. Describe the property used to convert the equation from one line to the next:
b. Why are we sure that the initial equation x(1 - x) + 2x - 4 = 8x - 24 - x² and the final equation 20 = 5x have the same solution set?
c. What is the common solution set to all these equations?

Exercise 2
Solve the equation for . For each step, describe the operation used to convert the equation.
3x - [8 - 3(x - 1)] = x + 19

Exercise 3
Solve each equation for x. For each step, describe the operation used to convert the equation.

Exercise 4
Consider the equations x + 1 = 4 and (x + 1)² = 16.
a. Verify x = 3 that is a solution to both equations.
b. Find a second solution to the second equation.
c. Based on your results, what effect does squaring both sides of an equation appear to have on the solution set?

Exit Ticket

1. Solve the equation for x. For each step, describe the operation and/or properties used to convert the equation.
   5(2x - 4) - 11 = 4 + 3x
2. Consider the equation x + 4 = 3x + 2
   a. Show that adding x + 2 to both sides of the equation does not change the solution set.
   b. Show that multiplying both sides of the equation by x + 2 adds a second solution of x = -2 to the solution set.

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