Page 500 #15-32 ANSWERS

1. Page 500 #15-32 ANSWERS

2. Student Progress Chart Lesson Reflection

4. Today’s Learning Goal Assignment Learn to solve multistep equations.

5. Pre-Algebra HW Page 504 #12-24

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

7. Solving Multistep Equations 10-2 y 15 Pre-Algebra Warm Up Solve. 1.3x = 102 2. = 15 3.z – 100 = –1 4. 1.1 + 5w = 98.6 x = 34 y = 225 z = 99 w = 19.5

8. 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

9. Today’s Learning Goal Assignment Learn to solve multistep equations.

10. To solve a complicated equation, you may have to simplify the equation first by combining like terms.

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

12. ? 8(3) + 6 + 3(3) – 2 = 37 ? 24 + 6 + 9 – 2 = 37 ? 37 = 37 Additional Example 1 Continued Check 8x + 6 + 3x – 2 = 37 Substitute 3 for x. 

13. 39 13x = 13 13 Try This: Example 1 Solve. 9x + 5 + 4x – 2 = 42 13x + 3 = 42 Combine like terms. – 3– 3Subtract to undo addition. 13x = 39 Divide to undo multiplication. x = 3

14. ? 9(3) + 5 + 4(3) – 2 = 42 ? 27 + 5 + 12 – 2 = 42 ? 42 = 42 Try This: Example 1 Continued Check 9x + 5 + 4x – 2 = 42 Substitute 3 for x. 

15. 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.

16. 7 7 7 –3 3 –3 4 4 4 4 4 4 5n 5n 5n 4 4 4 4 + = 4 ( )( )( ) 4 + 4 = 4 Additional Example 2: Solving Equations That Contain Fractions Solve. A. + = – Multiply both sides by 4 to clear fractions, and then solve. ( )( ) Distributive Property. 5n + 7 = –3

17. –10 Divide to undo multiplication. 5 5n = 5 Additional Example 2 Continued 5n + 7 = –3 – 7–7Subtract to undo addition. 5n = –10 n = –2

18. Remember! The least common denominator (LCD) is the smallest number that each of the denominators will divide into.

19. 18+ – = 18 ( ) x 7x 2 9 17 x 17 2 2 2 9 9 3 3 x 7x 2 9 7x 9 18( ) + 18( ) – 18( ) = 18( ) 2 17 3 9 Additional Example 2B: Solving Equations That Contain Fractions Solve. B. + – = The LCD is 18. Multiply both sides by the LCD. Distributive Property. 14x + 9x – 34 = 12 23x – 34 = 12 Combine like terms.

20. 46 = Divide to undo multiplication. 23 23x 23 Additional Example 2B Continued 23x – 34 = 12 Combine like terms. + 34+ 34Add to undo subtraction. 23x = 46 x = 2

21. x 7x 2 9 (2) ? + – = Substitute 2 for x. 2 17 17 6 17 2 17 2 2 2 2 9 17 9 9 9 3 9 3 9 9 3 3 9 2 ? ? ? 14 14 7(2) 14 + – = + – = + – = 9 9 9 9 1 ? = 6 6 9 9 The LCD is 9. Additional Example 2B Continued Check + – = 

22. 5 5 5 –1 1 –1 4 4 4 4 4 4 3n 3n 3n 4 4 4 4 + = 4 ( )( )( ) 4 + 4 = 4 Try This: Example 2A Solve. A. + = – Multiply both sides by 4 to clear fractions, and then solve. ( )( ) Distributive Property. 3n + 5 = –1

23. –6 Divide to undo multiplication. 3 3n = 3 Try This: Example 2A Continued 3n + 5 = –1 – 5–5Subtract to undo addition. 3n = –6 n = –2

24. x 5x 3 9 13 x 13 1 1 9+ – = 9( ) 3 9 ( ) 3 9 3 x 5x 3 9 5x 9( ) + 9( )– 9( ) = 9( ) 9 1 13 3 9 Try This: Example 2B Solve. B. + – = The LCD is 9. Multiply both sides by the LCD. Distributive Property. 5x + 3x – 13 = 3 8x – 13 = 3 Combine like terms.

25. 16 = Divide to undo multiplication. 8 8x 8 Try This: Example 2B Continued 8x – 13 = 3 Combine like terms. + 13+ 13Add to undo subtraction. 8x = 16 x = 2

26. x 5x 3 9 (2) ? + – = Substitute 2 for x. 3 6 13 3 13 2 13 1 1 13 1 9 3 3 9 9 9 3 9 3 9 ? ? 10 10 5(2) + – = + – = 9 9 9 ? = 3 3 9 9 The LCD is 9. Try This: Example 2B Continued Check + – = 

27. Mr. Harris $+ Mrs. Harris $ – Mr. Harris spent – Mrs. Harris spent = amount left h + 2h – 26 – 54 = 46 Additional Example 3: Money Application 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? Let h represent the amount of money that Mr. Harris had when he left home. So Mrs. Harris had 2h when she left home.

28. + 80+80 Add 80 to both sides. 3h = 3 126 3 Additional Example 3 Continued 3h – 80 = 46 Combine like terms. 3h = 126 Divide both sides by 3. h = 42 Mr. Harris had $42 when he left home.

29. Mr. Wesner $ + Mrs. Wesner $ – Mr. Wesner spent – Mrs. Wesner spent = amount left h + 3h – 50 – 25 = 25 Try This: Example 3 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? Let h represent the amount of money that Mr. Wesner had when he left home. So Mrs. Wesner had 3h when she left home.

30. 4h = 4 100 4 Try This: Example 3 Continued 4h – 75 = 25 Combine like terms. + 75+75 Add 75 to both sides. 4h = 100 Divide both sides by 4. h = 25 Mr. Wesner had $25 when he left home.

31. 9 16 25 2x 5 x 6x 33 8 8 8 7 21 21 x = 1 Lesson Quiz 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? x = 3 x = –3.75 x = 28 4. – = $8.50