1. Solving Multi-Step Equations 7-2 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. Solving Multi-Step Equations 7-2 Warm Up Solve. 1. 3x = 102 2. = 15 3. z – 100 = 21 4. 1.1 + 5w = 98.6 x = 34 y = 225 z = 121 w = 19.5 y 15

3. Solving Multi-Step Equations 7-2 Problem of the Day Ana has twice as much money as Ben, and Ben has three times as much as Clio. Together they have $160. How much does each person have? Ana, $96; Ben, $48; Clio, $16

4. Solving Multi-Step Equations 7-2 Learn to solve multi-step equations.

5. Solving Multi-Step Equations 7-2 To solve a multi-step equation, you may have to simplify the equation first by combining like terms or by using the Distributive Property.

6. Solving Multi-Step Equations 7-2 Solve. 8x + 6 + 3x – 2 = 37 Additional Example 1A: Solving Equations That Contain Like Terms 11x + 4 = 37 Combine like terms. – 4 – 4 Subtract 4 from both sides. 11x = 33 x = 3 Divide both sides by 11. 33 11 11x 11 =

7. Solving Multi-Step Equations 7-2 Check Additional Example 1A Continued 8x + 6 + 3x – 2 = 37 8(3) + 6 + 3(3) – 2 = 37 ? 24 + 6 + 9 – 2 = 37 ? 37 = 37 ? Substitute 3 for x.

8. Solving Multi-Step Equations 7-2 Solve. 4(x – 6) + 7 = 11 Additional Example 1B: Solving Equations That Contain Like Terms 4(x – 6) + 7 = 11 Distributive Property + 17 +17 Add 17 to both sides. x = 7 Divide both sides by 4. 4x = 28 44 4(x) – 4(6) + 7 = 11 4x – 24 + 7 = 11 Simplify by multiplying: 4(x) = 4x and 4(6) = 24. 4x – 17 = 11 Simplify by adding: –24 + 7 = 17.

9. Solving Multi-Step Equations 7-2 Solve. 9x + 5 + 4x – 2 = 42 Check It Out: Example 1 13x + 3 = 42 Combine like terms. – 3 – 3 Subtract 3 from both sides. 13x = 39 x = 3 Divide both sides by 13. 39 13 13x 13 =

10. Solving Multi-Step Equations 7-2 Check Check It Out: Example 1 Continued 9x + 5 + 4x – 2 = 42 9(3) + 5 + 4(3) – 2 = 42 ? 27 + 5 + 12 – 2 = 42 ? 42 = 42 ? Substitute 3 for x.

11. Solving Multi-Step Equations 7-2 If an equation contains fractions, it may help to multiply both sides of the equation by the least common denominator (LCD) of the fractions. This step results in an equation without fractions, which may be easier to solve.

12. Solving Multi-Step Equations 7-2 The least common denominator (LCD) is the smallest number that each of the denominators will divide into. Remember!

13. Solving Multi-Step Equations 7-2 Solve. + – = Additional Example 2: Solving Equations That Contain Fractions 2 3 The LCD is 18. x 2 7x7x 9 17 9 18 ( ) + 18 ( ) – 18 ( ) = 18 ( ) 7x7x 9 x 2 17 9 2 3 14x + 9x – 34 = 12 23x – 34 = 12 Combine like terms. ( ) ( ) x 2 2 3 7x7x 9 17 9 18 + – = 18 Distributive Property. Multiply both sides by 18.

14. Solving Multi-Step Equations 7-2 Additional Example 2 Continued 23x = 46 = 23x 23 46 23 Divide both sides by 23. x = 2 + 34 + 34 Add 34 to both sides. 23x – 34 = 12 Combine like terms.

15. Solving Multi-Step Equations 7-2 Additional Example 2 Continued 6 9 6 9 = ? Check x 2 7x7x 9 17 9 + – = 2 3 2 3 Substitute 2 for x. 7(2) 9 + – = (2) 2 17 9 ? 2 3 14 9 + – = 2 2 17 9 ? 2 3 14 9 + – = 17 9 ? 1 The LCD is 9. 6 9 14 9 + – = 9 9 17 9 ?

16. Solving Multi-Step Equations 7-2 Solve. + = – Check It Out: Example 2A 1 4 5 4 3n3n 4 Multiply both sides by 4 to clear fractions, and then solve. ( ) ( ) 5 4 –1 4 3n3n 4 4 + = 4 ( ) ( ) ( ) 3n 4 5 4 –1 4 4 + 4 = 4 3n + 5 = –1 Distributive Property.

17. Solving Multi-Step Equations 7-2 Check It Out: Example 2A Continued 3n + 5 = –1 – 5 –5 Subtract 5 from both sides. 3n = –6 3n3n 3 –6 3 = Divide both sides by 3. n = –2

18. Solving Multi-Step Equations 7-2 Solve. + – = Check It Out: Example 2B 1 3 The LCD is 9. x 3 5x5x 9 13 9 9 ( ) + 9 ( ) – 9 ( ) = 9 ( ) 5x5x 9 x 3 13 9 1 3 5x + 3x – 13 = 3 8x – 13 = 3 Combine like terms. ( ) x 3 1 3 5x5x 9 13 9 9 + – = 9 ( ) Distributive Property. Multiply both sides by 9.

19. Solving Multi-Step Equations 7-2 8x = 16 = 8x8x 8 16 8 Divide both sides by 8. x = 2 + 13 + 13 Add 13 to both sides. 8x – 13 = 3 Combine like terms. Check It Out: Example 2B Continued

20. Solving Multi-Step Equations 7-2 3 9 3 9 = ? Check x 3 5x5x 9 13 9 + – = 1 3 1 3 Substitute 2 for x. 5(2) 9 + – = (2) 3 13 9 ? 1 3 10 9 + – = 2 3 13 9 ? The LCD is 9. 3 9 10 9 + – = 6 9 13 9 ? Check It Out: Example 2B Continued

21. Solving Multi-Step Equations 7-2 On Monday, David rides his bicycle m miles in 2 hours. On Tuesday, he rides three times as far in 5 hours. If his average speed for the two days is 12 mi/h, how far did he ride on Monday? Round your answer to the nearest tenth of a mile. Additional Example 3: Travel Application David’s average speed is his total distance for the two days divided by the total time. average speed = Total distance Total time

22. Solving Multi-Step Equations 7-2 Additional Example 3 Continued Multiply both sides by 7. Substitute m + 3m for total distance and 2 + 5 for total time. 2 + 5 = 12 m + 3m 7 = 12 4m Simplify. 7 = 7(12) 7 4m 4m = 84 David rode 21.0 miles. Divide both sides by 4. m = 21 84 4 4m44m4 =

23. Solving Multi-Step Equations 7-2 Check It Out! Example 3 Penelope’s average speed is her total distance for the two days divided by the total time. average speed = Total distance Total time On Saturday, Penelope rode her scooter m miles in 3 hours. On Sunday, she rides twice as far in 7 hours. If her average speed for two days is 20 mi/h, how far did she ride on Saturday? Round your answer to the nearest tenth of a mile.

24. Solving Multi-Step Equations 7-2 Check It Out! Example 3 Continued Multiply both sides by 10. Substitute m + 2m for total distance and 3 + 7 for total time. 3 + 7 = 20 m + 2m 10 = 20 3m Simplify. 10 = 10(20) 10 3m 3m = 200 Penelope rode approximately 66.7 miles. Divide both sides by 3. m  66.67 200 3 3m33m3 =

25. Solving Multi-Step Equations 7-2 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

26. Solving Multi-Step Equations 7-2 Solve. 1. 6x + 3x – x + 9 = 33 2. 8(x + 2) + 5 = 29 3. + = 5. Linda is paid double her normal hourly rate for each hour she works over 40 hours in a week. Last week she worked 52 hours and earned $544. What is her hourly rate? Lesson Quiz x = 1 x = 3 x = 28 5 8 x 8 33 8 6x6x 7 4. – = 2x2x 21 25 21 $8.50 x = 1 9 16

27. Solving Multi-Step Equations 7-2 1. Solve 4p + 13 + 11p = 88 A. p = 5 B. p = 7 C. p = 75 D. p = 91 Lesson Quiz for Student Response Systems

28. Solving Multi-Step Equations 7-2 2. Solve 4(x + 3) + 5 = 109 A. x = 4 B. x = 23 C. x = 26 D. x = 101 Lesson Quiz for Student Response Systems

29. Solving Multi-Step Equations 7-2 3. Solve. A. x = 5 B. x = 6 C. x = 21 D. x = 101 Lesson Quiz for Student Response Systems