1. Solving two-step equations Chapter 4.1 Arizona State Standard – S3C3PO3 – Analyze situations, simplify, and solve problems involving linear equations and inequalities using the properties of the real number system.

2. Objective I will use two operations to solve a two step equation. I will solve real-life problems using two step equations.

3. Ultimate Goal ISOLATE THE VARIABLE Ask yourself??? How is the variable attached?

4. Addition property of equality Addition property of equality 2 x + 5 = 9 2x + 5 -5 = 9 -5 2x = 4 2 2 2 2 x = 2 Subtract 5 from both sides Simplify Divide both sides by 2 Simplify

5. Check To see that 2 is the solution, replace x in the original equation with 2. 2 x + 5 = 9 2 (2) + 5 = 9 4 + 5 = 9 9 = 9

6. Give it a try 3 x + 6 = 12 3x + 6 – 6 = 12 –6 3x = 6 3 3 x = 2

7. Give it a try! 4.5 = 3 + 2.5 x 4.5 – 3 = 3 + 2.5 x – 3 1.5 = 2.5 x 2.5 2.5 0.6 = x

8. Check 0.6 = 2 – 3.5c 0.6 = 2 – 3.5 (0.4) 0.6 = 2 – 1.4 0.6 = 0.6

9. Real-Life Situation You are joining a community tennis club. The annual membership fee is $50, and a tennis court rents for $10 per hour. You plan to spend no more than $190 playing tennis during the year. How many hours can you play? Step 1: Translate: Total spent = annual fee + hourly rate x hours of tennis

10. You are joining a community tennis club. The annual membership fee is $50, and a tennis court rents for $10 per hour. You plan to spend no more than $190 playing tennis during the year. How many hours can you play? Total spent = annual fee + hourly rate x hours of tennis Step 2: Label the constants, identify the variable Total spent = $190 Annual Fee = $50 Hourly Rate = $10 Number of hours played = n

11. You are joining a community tennis club. The annual membership fee is $50, and a tennis court rents for $10 per hour. You plan to spend no more than $190 playing tennis during the year. How many hours can you play? Total spent = annual fee + hourly rate x hours of tennis Step 3: Substitute the constants into the algebraic equation. 190 = 50 + 10 x n

12. Step 4: Isolate the variable 190 = 50 + 10 x n 190 – 50 = 50 – 50 + 10 x n 140 = 10 x n 10 10 14 = n

13. Does it make sense? The question asked….How many hours can you play for $190? There is a $50 membership fee and each hour on the court cost $10. Does the answer of 14 hours make sense???

14. Practice Page 160 #1 – 3 # 9 - 24

15. Chapter 4.2 Solving Multi-Step Equations

16. Objective I will combine like terms and use the distributive property to solve equations.

17. Ultimate Goal ISOLATE THE VARIABLE Ask yourself??? How is the variable attached?

18. Combing Like Terms Before using inverse operations to solve an equation, you should check to see whether one or both sides of the equation can be simplified by combining like terms. Like Terms – Two or more terms in an expression that have the same variables raised to the same powers.

19. Solve – Combining Like Terms -13 = 3 n + 3 + n -13 = 4 n + 3 -16 = 4 n -4 = n

20. Solve – Combining like terms -6 x – 1 + 5x = 3 -x – 1 = 3 -x – 1 + 1 = 3 + 1 -x = 4 -1 -1 x = -4

21. Give it a try! -2x + 2 – 4x = 20 -6x + 2 = 20 -6x + 2 – 2 = 20 – 2 -6x = 18 -6 -6 x = -3

22. Distributive Property 2 (x – 3) = 10 2x – 6 = 10 2x – 6 + 6 = 10 + 6 2x = 16 2 2 x = 8

23. Give it a try! 4 (x – 2) = 10 4x – 8 = 10 4x = 18 x = 18 ÷ 4 x = 4 ½

24. Distributing a Negative 2 – (3x - 4) = 2 It can help to rewrite – as -1

25. Practice Time Practice Time Page 164 # 1 – 6, 19 1. 3x – x + 8 = -16 Step 1: Combine like terms 3x – x = 2x 2x+ 8 =16 2x+ 8 =16 Step 2: Inverse Operation (subtract 8) 2x + 8 – 8 = -16 - 8 *Whatever you do to one side, you MUST do to the other. *Remember to Keep, Change, Change 2x = -24 2x = -24 Step 3: Inverse Operation (Divide by 2) 2x ÷ 2 = -24 ÷ 2 *Remember: Different Sign NEGATIVE x = -12 *Remember: Different Sign NEGATIVE x = -12 HOMEWORK # 7 - 21

26. Practice Time Practice Time Page 164 # 1 – 6, 19 19. 5 – 3 (x + 1) = 5 Step 1: Use the Distributive Property to get rid of the parenthesis -3(x+1) = -3x - 3 Step 2: Rewrite the problem 5 -3x – 3 = 5 Step 3: Combine like terms 5 + -3 = 2 Step 4: Rewrite the problem 2 – 3x = 5 OR -3X + 2 = 5 Step 5: Inverse Operation (subtract 2) *Whatever you do to one side, you MUST do to the other. *Remember to Keep, Change, Change