1. Holt CA Course 1 11-3Solving Multi-Step Equations Preview of Grade 7 AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, and commutative) and justify the process used. Also covered: Preview of Algebra 1 5.0 California Standards

2. Holt CA Course 1 11-3Solving Multi-Step Equations Solve 12 – 7b + 10b = 18. Teacher Example 1: Combining Like Terms to Solve Equations 12 – 7b + 10b = 18 12 + 3b = 18 – 12 3b = 6 3 b = 2 Combine like terms. Subtract 12 from both sides. Divide both sides by 3.

3. Holt CA Course 1 11-3Solving Multi-Step Equations Solve 14 – 8b + 12b = 62. 14 – 8b + 12b = 62 14 + 4b = 62 – 14 4b = 48 4 b = 12 Combine like terms. Subtract 14 from both sides. Divide both sides by 4. Student Practice 1:

4. Holt CA Course 1 11-3Solving Multi-Step Equations You may need to use the Distributive Property to solve an equation that has parentheses. Multiply each term inside the parentheses by the factor that is outside the parentheses. Then combine like terms.

5. Holt CA Course 1 11-3Solving Multi-Step Equations Solve 5(y – 2) + 6 = 21. Teacher Example 2: Using the Distributive Property to Solve Equations 5(y – 2) + 6 = 21 5(y) – 5(2) + 6 = 21 + 4 + 4 5y = 25 5 y = 5 Distribute 5 on the left side. Simplify. Add 4 to both sides. 5y – 10 + 6 = 21 Divide both sides by 5. Combine like terms. 5y – 4 = 21

6. Holt CA Course 1 11-3Solving Multi-Step Equations The Distributive Property states that a(b + c) = ab + ac. For instance, 2(3 + 5) = 2(3) + 2(5). Remember!

7. Holt CA Course 1 11-3Solving Multi-Step Equations Solve 3(x – 3) + 4 = 28. Student Practice 2: 3(x – 3) + 4 = 28 3(x) – 3(3) + 4 = 28 + 5 3x = 33 3 x = 11 Distribute 3 on the left side. Simplify. Add 5 to both sides. 3x – 9 + 4 = 28 Divide both sides by 3. Combine like terms. 3x – 5 = 28

8. Holt CA Course 1 11-3Solving Multi-Step Equations Troy has three times as many trading cards as Hillary. Subtracting 8 from the combined number of trading cards Troy and Hillary have gives the number of cards Sean has. If Sean owns 24 trading cards, how many trading cards does Hillary own? Teacher Example 3: Problem Solving Application

9. Holt CA Course 1 11-3Solving Multi-Step Equations Teacher Example 3 Continued 1 Understand the Problem Rewrite the question as a statement. Find the number of trading cards that Hillary owns. List the important information: Troy owns 3 times as many trading cards as Hillary. Subtracting 8 from the combined number of trading cards Troy and Hillary own gives the number cards Sean owns. Sean owns 24 trading cards.

10. Holt CA Course 1 11-3Solving Multi-Step Equations2 Make a Plan Let c represent the number of trading cards Hillary owns. Then 3c represents the number Troy owns. Troy’s cards + Hillary’s cards – 8 = Sean’s cards 3c + c – 8 = 24 Solve the equation 3c + c – 8 = 24 for c. Teacher Example 3 Continued

11. Holt CA Course 1 11-3Solving Multi-Step Equations Solve 3 3c + c – 8 = 24 4c – 8 = 24 + 8 4c = 32 44 c = 8 Hillary owns 8 cards. Combine like terms. Add 8 to both sides. Divide both sides by 4. Teacher Example 3 Continued 4c = 32

12. Holt CA Course 1 11-3Solving Multi-Step Equations Look Back 4 Make sure that your answer makes sense in the original problem. Hillary owns 8 cards. Troy owns 3(8) = 24 cards. Sean owns 24 + 8 – 8 = 24. Teacher Example 3 Continued

13. Holt CA Course 1 11-3Solving Multi-Step Equations Student Practice 3: John is twice as old as Hiro. Subtracting 4 from the combined age of John and Hiro gives William’s age. If William is 29, how old is Hiro?

14. Holt CA Course 1 11-3Solving Multi-Step Equations Student Practice 3: 1 Understand the Problem Rewrite the question as a statement. Find Hiro’s age. List the important information: John is 2 times as old as Hiro. Subtracting 4 from the combined age of John and Hiro gives William’s age. William is 29 years old.

15. Holt CA Course 1 11-3Solving Multi-Step Equations2 Make a Plan Let h represent Hiro’s age. Then 2h represents John’s age. John’s age + Hiro’s age – 4 = William’s age 2h + h – 4 = 29 Solve the equation 2h + h – 4 = 29. Student Practice 3:

16. Holt CA Course 1 11-3Solving Multi-Step Equations Solve 3 2h + h – 4 = 29 3h – 4 = 29 + 4 3h = 33 33 h = 11 Hiro is 11 years old. Combine like terms. Add 4 to both sides. Divide both sides by 3. 3h = 33 Student Practice 3:

17. Holt CA Course 1 11-3Solving Multi-Step Equations Look Back 4 Make sure that your answer makes sense in the original problem. Hiro is 11 years old, then John is 2(11) = 22 years old. William is 22 + 11 – 4 = 29 years old. Student Practice 3:

18. Holt CA Course 1 11-3Solving Multi-Step Equations 11.3 Warm-Up Solve. 1. –x – 11 + 17x = 53 2. 4(k – 3) + 1 = 33 3. Kelly swam 4 times as many laps as Kathy. Adding 5 to the number of laps Kelly swam gives you the number of laps Julie swam. If Julie swam 9 laps, how many laps did Kathy swim?

19. Holt CA Course 1 11-3Solving Multi-Step Equations 11.3 Day 2 Warm-Up Solve. 1. c + 21 + 5c = 63 2. 59 = w – 16 + 4w 5. Ann earns 1.5 times her normal hourly pay for each hour that she works over 40 hours in a week. Last week she worked 51 hours and earned $378.55. What is her normal hourly pay?