1. Pre-Algebra 10-2 Solving Multistep Equations 10-2 Solving Multistep Equations Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Pre-Algebra 10-2 Solving Multistep Equations Warm Up Solve. 1. 3x = 102 2. = 15 3. z – 100 = –1 4. 1.1 + 5w = 98.6 x = 34 y = 225 z = 99 Pre-Algebra 10-2 Solving Multistep Equations w = 19.5 y 15

3. Pre-Algebra 10-2 Solving Multistep Equations 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. Pre-Algebra 10-2 Solving Multistep Equations Learn to solve multistep equations.

5. Pre-Algebra 10-2 Solving Multistep Equations To solve a complicated equation, you may have to simplify the equation first by combining like terms.

6. Pre-Algebra 10-2 Solving Multistep Equations Solve. 8x + 6 + 3x – 2 = 37 Additional Example 1: Solving Equations That Contain Like Terms 11x + 4 = 37 Combine like terms. – 4 – 4 Subtract to undo addition. 11x = 33 x = 3 Divide to undo multiplication. 33 11 11x 11 =

7. Pre-Algebra 10-2 Solving Multistep Equations Check Additional Example 1 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. Pre-Algebra 10-2 Solving Multistep Equations Solve. 9x + 5 + 4x – 2 = 42 Try This: Example 1 13x + 3 = 42 Combine like terms. – 3 – 3 Subtract to undo addition. 13x = 39 x = 3 Divide to undo multiplication. 39 13 13x 13 =

9. Pre-Algebra 10-2 Solving Multistep Equations Check Try This: 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.

10. Pre-Algebra 10-2 Solving Multistep Equations If an equation contains fractions, it may help to multiply both sides of the equation by the least common denominator (LCD) to clear the fractions before you isolate the variable.

11. Pre-Algebra 10-2 Solving Multistep Equations Solve. A. + = – Additional Example 2: Solving Equations That Contain Fractions 3 4 7 4 5n5n 4 Multiply both sides by 4 to clear fractions, and then solve. ( ) ( ) 7 4 –3 4 5n5n 4 4 + = 4 ( ) ( ) ( ) 5n 4 7 4 –3 4 4 + 4 = 4 5n + 7 = –3 Distributive Property.

12. Pre-Algebra 10-2 Solving Multistep Equations Additional Example 2 Continued 5n + 7 = –3 – 7 –7 Subtract to undo addition. 5n = –10 5n5n 5 –10 5 = Divide to undo multiplication. n = –2

13. Pre-Algebra 10-2 Solving Multistep Equations The least common denominator (LCD) is the smallest number that each of the denominators will divide into. Remember!

14. Pre-Algebra 10-2 Solving Multistep Equations Solve. B. + – = Additional Example 2B: 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 the LCD.

15. Pre-Algebra 10-2 Solving Multistep Equations Additional Example 2B Continued 23x = 46 = 23x 23 46 23 Divide to undo multiplication. x = 2 + 34 + 34 Add to undo subtraction. 23x – 34 = 12 Combine like terms.

16. Pre-Algebra 10-2 Solving Multistep Equations Additional Example 2B 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 ?

17. Pre-Algebra 10-2 Solving Multistep Equations Solve. A. + = – Try This: 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.

18. Pre-Algebra 10-2 Solving Multistep Equations Try This: Example 2A Continued 3n + 5 = –1 – 5 –5 Subtract to undo addition. 3n = –6 3n3n 3 –6 3 = Divide to undo multiplication. n = –2

19. Pre-Algebra 10-2 Solving Multistep Equations Solve. B. + – = Try This: 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 the LCD.

20. Pre-Algebra 10-2 Solving Multistep Equations 8x = 16 = 8x8x 8 16 8 Divide to undo multiplication. x = 2 + 13 + 13 Add to undo subtraction. 8x – 13 = 3 Combine like terms. Try This: Example 2B Continued

21. Pre-Algebra 10-2 Solving Multistep Equations 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 ? Try This: Example 2B Continued

22. Pre-Algebra 10-2 Solving Multistep Equations When Mr. and Mrs. Harris left for the mall, Mrs. Harris had twice as much money as Mr. Harris had. While shopping, Mrs. Harris spent $54 and Mr. Harris spent $26. When they arrived home, they had a total of $46. How much did Mr. Harris have when he left home? Additional Example 3: Money Application Let h represent the amount of money that Mr. Harris had when he left home. So Mrs. Harris had 2h when she left home. h + 2h – 26 – 54 = 46 Mr. Harris $+ Mrs. Harris $ – Mr. Harris spent – Mrs. Harris spent = amount left

23. Pre-Algebra 10-2 Solving Multistep Equations Additional Example 3 Continued 3h – 80 = 46Combine like terms. + 80 +80Add 80 to both sides. 3h = 126 3h3h 3 126 3 = Divide both sides by 3. h = 42 Mr. Harris had $42 when he left home.

24. Pre-Algebra 10-2 Solving Multistep Equations When Mr. and Mrs. Wesner left for the store, Mrs. Wesner had three times as much money as Mr. Wesner had. While shopping, Mr. Wesner spent $50 and Mrs. Wesner spent $25. When they arrived home, they had a total of $25. How much did Mr. Wesner have when he left home? Try This: Example 3 Let h represent the amount of money that Mr. Wesner had when he left home. So Mrs. Wesner had 3h when she left home. h + 3h – 50 – 25 = 25 Mr. Wesner $ + Mrs. Wesner $ – Mr. Wesner spent – Mrs. Wesner spent = amount left

25. Pre-Algebra 10-2 Solving Multistep Equations Try This: Example 3 Continued 4h – 75 = 25Combine like terms. + 75 +75Add 75 to both sides. 4h = 100 4h4h 4 100 4 = Divide both sides by 4. h = 25 Mr. Wesner had $25 when he left home.

26. Pre-Algebra 10-2 Solving Multistep Equations Tell how you would clear the fractions in the equation.

27. Pre-Algebra 10-2 Solving Multistep Equations Journal: Compare the process of solving a multistep equation with the process of checking the solution.

28. Pre-Algebra 10-2 Solving Multistep Equations Solve. 1. 6x + 3x – x + 9 = 33 2. –9 = 5x + 21 + 3x 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 = –3.75 x = 3 x = 28 5 8 x 8 33 8 6x6x 7 4. – = 2x2x 21 25 21 $8.50 x = 1 9 16