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.
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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