1. Bell Work: Factor 9x + 81x 2

2. Answer: 9x(1 + 9)

3. Lesson 38: Using Properties of Equality to Solve Equations

4. We have practiced solving equations by inspection using logical reasoning. In this lesson we will use inverse operations to solve equations.

5. Inverse operations “undo” each other.

6. Addition and subtraction are inverse operations (n + 5 – 5 = n) Multiplication and division are inverse operations (n x 5 ÷ 5 = n) Any number may be used for n in the equations above to perform the operations. The result in every case is n.

7. We use inverse operations to isolate the variable in an equation. Example: x + 5 = 12 -5 -5 x = 7

8. Isolating a variable means that the variable, like x, is “alone” on one side of the equals sign. There are 2 aspects of isolating a variable.

9. 1.We choose the operation that isolates the variable 2.We perform the operation on both sides of the equals sign to keep the equation balanced

10. Performing the same operation on both sides of an equation preserves the equality of the equation. The are four properties of equality we can use to manipulate equations.

11. Operation Properties of Equality Addition: if a = b, then a + c = b + c Subtraction: if a = b, then a – c = b – c Multiplication: if a = b, then ac = bc Division: if a = b, then a/c = b/c if c is not 0

12. Example: After spending $2.30, Robert had $5.70. How much money did he have before he spent $2.30? Solve this equation to find the answer: x – 2.30 = 5.70

13. Answer: x – 2.30 = 5.70 +2.30 +2.30 x = $8.00

14. Example: If a 12-month subscription to a magazine costs $8.40, what is the average cost per month? Solve this equation to find the answer. 12m = 8.40

15. Answer: 12m = 8.40 12 12 m = $0.70 per month

16. Example: Solve 2/3 w = 3/4

17. Answer: 2/3 w(3/2) = 3/4(3/2) w = 9/8 = 1 1/8

18. It is customary to express a solution with the variable on the left side of the equal sign. Since the quantities on either side of an equal sign are equal, we can reverse everything on one side of an equation of an equation with everything on the other side of the equation.

19. This property of equality is called the symmetric property. Symmetric Property of Equality If a = b, then b = a

20. Example: Solve 1.5 = x – 2.3

21. Answer: 1.5 = x – 2.3 +2.3 +2.3 3.8 = x x = 3.8

22. HW: Lesson 38 #1-30