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10-2 10-2Solving SolvingMultistep MultistepEquations Equations Homework & Learning Goal Lesson Presentation 6th Grade AIMS Prep Pre-Algebra Pre-Algebra 10-2 Solving Multistep Equations PA HOMEWORK ANSWERS Page 500 #8-30 EVENS Pre-Algebra 10-2 Solving Multistep Equations Pre-Algebra HOMEWORK Page 504 #12-30 EVENS Pre-Algebra 10-2 Solving Multistep Equations Our Learning Goal Students will be able to solve multi-step equations with multiple variables, solve inequalities and graph the solutions on a number line. Pre-Algebra 10-2 Solving Multistep Equations Our Learning Goal Assignments • Learn to solve two-step equations. • Learn to solve multistep equations. • Learn to solve equations with variables on both sides of the equal sign. • Learn to solve two-step inequalities and graph the solutions of an inequality on a number line. • Learn to solve an equation for a variable. • Learn to solve systems of equations. Pre-Algebra 10-2 Solving Multistep Equations Today’s Learning Goal Assignment Learn to solve multistep equations. Pre-Algebra 10-2 Solving Multistep Equations REMEMBER!! To solve a complicated equation, you may have to simplify the equation first by combining like terms. Pre-Algebra 10-2 Solving Multistep Equations Additional Example 1: Solving Equations That Contain Like Terms Solve. 8x + 6 + 3x – 2 = 37 11x + 4 = 37 Combine like terms. – 4 – 4 Subtract to undo addition. 11x = 33 11x = 33 Divide to undo multiplication. 11 11 x=3 Pre-Algebra 10-2 Solving Multistep Equations Additional Example 1 Continued Check 8x + 6 + 3x – 2 = 37 ? 8(3) + 6 + 3(3) – 2 = 37 Substitute 3 for x. ? 24 + 6 + 9 – 2 = 37 ? 37 = 37 Pre-Algebra 10-2 Solving Multistep Equations Try This: Example 1 Solve. 9x + 5 + 4x – 2 = 42 13x + 3 = 42 Combine like terms. – 3 – 3 Subtract to undo addition. 13x = 39 13x = 39 Divide to undo multiplication. 13 13 x=3 Pre-Algebra 10-2 Solving Multistep Equations Try This: Example 1 Continued Check 9x + 5 + 4x – 2 = 42 ? 9(3) + 5 + 4(3) – 2 = 42 Substitute 3 for x. ? 27 + 5 + 12 – 2 = 42 ? 42 = 42 Pre-Algebra 10-2 Solving Multistep Equations ANOTHER THANG to REMEMBER 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. Pre-Algebra 10-2 Solving Multistep Equations O’Wait, another thingy to Remember! The least common denominator (LCD) is the smallest number that each of the denominators will divide into. Pre-Algebra 10-2 Solving Multistep Equations Additional Example 2: Solving Equations That Contain Fractions Solve. A. 5n+ 7 = – 3 4 4 4 Multiply both sides by 4 to clear fractions, and then solve. 4 5n + 7 = 4 –3 4 4 4 ( ) ( ) 7 = 4 –3 Distributive Property. 4(5n + 4 (4 ) (4) 4) 5n + 7 = –3 Pre-Algebra 10-2 Solving Multistep Equations Additional Example 2 Continued 5n + 7 = –3 – 7 –7 Subtract to undo addition. 5n = –10 5n= –10 5 5 n = –2 Pre-Algebra Divide to undo multiplication. 10-2 Solving Multistep Equations Try This: Example 2A Solve. A. 3n+ 5 = – 1 4 4 4 Multiply both sides by 4 to clear fractions, and then solve. 4 3n + 5 = 4 –1 4 4 4 ( ) ( ) 5 = 4 –1 4(3n + 4 (4 ) (4) 4) 3n + 5 = –1 Pre-Algebra Distributive Property. 10-2 Solving Multistep Equations Try This: Example 2A Continued 3n + 5 = –1 – 5 –5 3n = –6 3n= –6 3 3 n = –2 Pre-Algebra Subtract to undo addition. Divide to undo multiplication. 10-2 Solving Multistep Equations Additional Example 2B: Solving Equations That Contain Fractions Solve. B. 7x + x – 17 = 2 3 2 9 9 The LCD is 18. Multiply both 17 7x x 2 18 + – = 18 sides by the LCD. 9 2 9 3 7x x 17 2 Distributive 18 9 + 18 2 – 18 9 = 18 3 Property. () ( () ) () () 14x + 9x – 34 = 12 23x – 34 = 12 Combine like terms. Pre-Algebra 10-2 Solving Multistep Equations Additional Example 2B Continued 23x – 34 = 12 Combine like terms. + 34 + 34 23x = 46 23x = 46 23 23 Add to undo subtraction. x=2 Pre-Algebra Divide to undo multiplication. 10-2 Solving Multistep Equations Additional Example 2B Continued Check 7x + x – 17 = 2 2 3 9 9 ? 2 7(2) + (2) – 17 = Substitute 2 for x. 9 2 9 3 14 2 17 ? 2 9 +2 – 9 =3 ? 2 14 + 1 – 17 = 9 9 3 14 9 17 ? 6 The LCD is 9. 9 +9 – 9 =9 ? 6 6= 9 9 Pre-Algebra 10-2 Solving Multistep Equations Try This: Example 2B Solve. B. 5x + x – 13 = 1 3 3 9 9 The LCD is 9. 1 13 5x x 9 + – =9 3 9 3 9 5x x 13 1 9 9 +9 3 –9 9 =9 3 ( ) () () () () () Multiply both sides by the LCD. Distributive Property. 5x + 3x – 13 = 3 8x – 13 = 3 Combine like terms. Pre-Algebra 10-2 Solving Multistep Equations Try This: Example 2B Continued 8x – 13 = 3 + 13 + 13 8x = 16 8x = 16 8 8 x=2 Pre-Algebra Combine like terms. Add to undo subtraction. Divide to undo multiplication. 10-2 Solving Multistep Equations Try This: Example 2B Continued Check 5x + x – 13 = 1 3 3 9 9 ? 1 5(2) + (2) – 13 = Substitute 2 for x. 9 3 9 3 10 2 13 ? 1 9 +3 – 9 =3 ? 3 10 + 6 – 13 = The LCD is 9. 9 9 9 9 ? 3 3= 9 9 Pre-Algebra 10-2 Solving Multistep Equations 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. h + 2h – 26 – 54 = 46 Pre-Algebra Mr. Harris $+ Mrs. Harris $ – Mr. Harris spent – Mrs. Harris spent = amount left 10-2 Solving Multistep Equations Additional Example 3 Continued 3h – 80 = 46 + 80 +80 3h = 126 3h 126 3= 3 h = 42 Combine like terms. Add 80 to both sides. Divide both sides by 3. Mr. Harris had $42 when he left home. Pre-Algebra 10-2 Solving Multistep Equations 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. Mr. Wesner $ + Mrs. Wesner $ h + 3h – 50 – 25 = 25 – Mr. Wesner spent – Mrs. Wesner spent = amount left Pre-Algebra 10-2 Solving Multistep Equations Try This: Example 3 Continued 4h – 75 = 25 + 75 +75 4h = 100 4h 100 4= 4 h = 25 Combine like terms. Add 75 to both sides. Divide both sides by 4. Mr. Wesner had $25 when he left home. Pre-Algebra 10-2 Solving Multistep Equations Don’t forget your proper heading! Trade & Grade! 10-2 Lesson Quiz Solve. 1. 6x + 3x – x + 9 = 33 x = 3 2. –9 = 5x + 21 + 3x 3. 5 + x = 33 8 8 8 4. 6x – 2x = 25 7 21 21 x = –3.75 x = 28 9 x = 116 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? $8.50 Pre-Algebra th 6 Grade AIMS Prep Recall some test-taking tricks that you use to “win” on the AIMS Math. Use at least one to solve the following example! AIMS Example 2