1. Unit 2 – Week 4 Reasoning with Linear Equations and Inequalities Lesson 3 Students are introduced to the formal process of solving an equation: starting from the assumption that the original equation has a solution. Students explain each step by following the properties of equality. Students identify equations that have the same solution set.

2. Standards A.REI.1 – Using algebraic properties and the properties of real numbers, justify the steps of a simple one-solution equation. A.REI.3 – Solve linear equations in one variable including equations with coefficients represented by letters.

3. Essential Questions What are properties of equality? How are the properties of equality used to solve equations?

4. Vocabulary Words Properties of Equality: Rules that allow you to balance, manipulate and solve equations

5. Read, Write, Draw, Solve Sam says that the equation 5(x – 7) = -35 + 5x is not true because the two expression are NOT equivalent. Do you agree or disagree with Sam? Justify your answer.

6. Activator Solve the following equation and record your thinking as you perform each step. 8x + 12 = 28 Write your solution set in words, set notation and on a number line.

7. 7 Example 1 Which property of equality is missing in the steps to solve the equation –7x + 22 = 50? 2.1.1: Properties of Equality EquationSteps –7x + 22 = 50Original equation –7x = 28 x = –4Division property of equality

8. 8 Example 1, continued 1.Observe the differences between the original equation and the next equation in the sequence. What has changed? – Notice that 22 has been taken away from both expressions, –7x + 22 and 50. 2.1.1: Properties of Equality

9. 9 Example 1, continued 2.Refer to the table of Properties of Equality. – The subtraction property of equality tells us that when we subtract a number from both sides of the equation, the expressions remain equal. – The missing step is “Subtraction property of equality.” 2.1.1: Properties of Equality ✔

10. Guided Practice: Example 1, continued 2.1.1: Properties of Equality 10

11. 11 Example 2 Which property of equality is missing in the steps to solve the equation EquationSteps Original equation Addition property of equality –x = 42 x = –42Division property of equality

12. Example 2, continued 1.Observe the differences between the original equation and the next equation in the sequence. What has changed? Notice that 3 has been added to both expressions, and 4. The result of this step is. 2.1.1: Properties of Equality 12

13. Example 2, continued In order to move to the next step, the division of 6 has been undone. The inverse operation of the division of 6 is the multiplication of 6. The result of multiplying by 6 is –x and the result of multiplying 7 by 6 is 42. This matches the next step in the sequence. 2.1.1: Properties of Equality 13

14. Example 2, continued 2.Refer to the table of Properties of Equality. The multiplication property of equality tells us that when we multiply both sides of the equation by a number, the expressions remain equal. The missing step is “Multiplication property of equality.” 2.1.1: Properties of Equality 14 ✔

15. Guided Practice: Example 2, continued 2.1.1: Properties of Equality 15

16. Complete the Table EquationSteps 6 + x = 72Original Equation

17. Complete the Table EquationSteps Original Equation

18. Complete the Table EquationSteps -7x – 12 = 16Original Equation

19. Complete the Table EquationSteps 8 = 0.4x – 2Original Equation

20. Complete the Table EquationSteps 76 = 5x – 15 + 2xOriginal Equation 76 = 5x + 2x – 15

21. Complete the Table EquationSteps 5(5x – 2) = 50Original Equation

22. Complete the Table EquationSteps

23. Complete the Table EquationSteps Original Equation

24. Complete the Table EquationSteps 8(2x – 1) = 56

25. Complete the Table EquationSteps 5x + 3(x + 4) = 28

26. Summarizer 1.When we solved for x in the equation 5(5x – 2) = 50 we got x = 2. Explain what this solution means. 2.Josiah used the equation above to represent that he has $5 and multiplied that times the quantity of $5 for each book minus a $2 fee equaled $50. Explain what the variable means and what you solution means in relationship to this situation.