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10-2

Solving Multistep Equations. 10-2. Course 3. Warm Up. Problem of the Day. Lesson Presentation. Solving Multistep Equations. 10-2. y 15. Course 3. Warm Up Solve. 1. 3 x = 102 2. = 15 3. z – 100 = –1 4. 1.1 + 5 w = 98.6. x = 34. y = 225. z = 99. w = 19.5.

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10-2

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  1. Solving Multistep Equations 10-2 Course 3 Warm Up Problem of the Day Lesson Presentation

  2. Solving Multistep Equations 10-2 y 15 Course 3 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

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

  5. Solving Multistep Equations 10-2 Course 3 To solve a complicated equation, you may have to simplify the equation first by combining like terms.

  6. Solving Multistep Equations 10-2 33 11x = 11 11 Course 3 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

  7. Solving Multistep Equations 10-2 ? 8(3) + 6 + 3(3) – 2 = 37 ? 24 + 6 + 9 – 2 = 37 ? 37 = 37 Course 3 Additional Example 1 Continued Check 8x + 6 + 3x – 2 = 37 Substitute 3 for x. 

  8. Solving Multistep Equations 10-2 39 13x = 13 13 Course 3 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

  9. Solving Multistep Equations 10-2 ? 9(3) + 5 + 4(3) – 2 = 42 ? 27 + 5 + 12 – 2 = 42 ? 42 = 42 Course 3 Try This: Example 1 Continued Check 9x + 5 + 4x – 2 = 42 Substitute 3 for x. 

  10. Solving Multistep Equations 10-2 Course 3 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. Solving Multistep Equations 10-2 7 7 7 –3 –3 3 4 4 4 4 4 4 5n 5n 5n 4 4 4 4 + = 4 ( )( )( ) 4 + 4 = 4 Course 3 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

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

  13. Solving Multistep Equations 10-2 Remember! The least common denominator (LCD) is the smallest number that each of the denominators will divide into. Course 3 Insert Lesson Title Here

  14. Solving Multistep Equations 10-2 18+ – = 18 ( ) x 7x 2 9 x 17 2 2 17 2 9 9 3 3 x 7x 2 9 7x 9 18( ) + 18( ) – 18( ) = 18( ) 17 2 3 9 Course 3 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.

  15. Solving Multistep Equations 10-2 46 = Divide to undo multiplication. 23 23x 23 Course 3 Additional Example 2B Continued 23x – 34 = 12 Combine like terms. + 34+ 34Add to undo subtraction. 23x = 46 x = 2

  16. Solving Multistep Equations 10-2 x 7x 2 9 (2) ? + – = Substitute 2 for x. 2 17 17 2 2 17 2 2 2 6 17 9 17 3 9 9 3 9 9 3 9 9 3 9 2 ? ? ? 14 14 14 7(2) + – = + – = + – = 9 9 9 9 1 ? = 6 6 9 9 The LCD is 9. Course 3 Additional Example 2B Continued Check + – = 

  17. Solving Multistep Equations 10-2 5 5 5 –1 –1 1 4 4 4 4 4 4 3n 3n 3n 4 4 4 4 + = 4 ( )( )( ) 4 + 4 = 4 Course 3 Try This: Example 2A Solve. A. + = – Multiply both sides by 4 to clear fractions, and then solve. ( )( ) Distributive Property. 3n + 5 = –1

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

  19. Solving Multistep Equations 10-2 x 5x 3 9 13 x 13 1 1 9+ – = 9( ) 3 9 ( ) 3 3 9 x 5x 3 9 5x 9( ) + 9( )– 9( ) = 9( ) 9 13 1 3 9 Course 3 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.

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

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

  22. Solving Multistep Equations 10-2 Mr. Harris $+ Mrs. Harris $ – Mr. Harris spent – Mrs. Harris spent = amount left h + 2h – 26 – 54 = 46 Course 3 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.

  23. Solving Multistep Equations 10-2 + 80+80 Add 80 to both sides. 3h = 3 126 3 Course 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.

  24. Solving Multistep Equations 10-2 Mr. Wesner $ + Mrs. Wesner $ – Mr. Wesner spent – Mrs. Wesner spent = amount left h + 3h – 50 – 25 = 25 Course 3 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.

  25. Solving Multistep Equations 10-2 4h = 4 100 4 Course 3 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.

  26. Solving Multistep Equations 10-2 9 16 25 2x 33 x 6x 5 21 8 21 7 8 8 x = 1 Course 3 Insert Lesson Title Here 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

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