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2.4 Solving Multi-Step Equations Indicators: PFA7, PFA8, PFA9 Written by ??? Edited by Eddie Judd, Crestwood Middle School Edited by Dave Wesley, Crestwood Middle School To Solve: Undo the operations by working backward. Ex: x + 9 = 6 5 Ask yourself: • What is the first thing we are doing to x? • The second thing? Recall the order of operations as you answer these questions. • dividing by 5 • adding 9 To undo these steps, do the opposite operations in opposite order. The DO-UNDO chart Use a chart as a shortcut to answering the questions. DO UNDO • ÷5 -9 • +9 ·5 Follow the steps in the ‘undo’ column to isolate the variable. Ex: x + 9 = 6 5 • First subtract 9. x+9-9=6-9 5 x = -3 5 • Then multiply by 5. (5) x = -3(5) 5 x = -15 Let’s try another! Complete the do-undo chart. DO UNDO • -2 ·3 • ÷3 +2 To solve for d: • First multiply by 3. • Then add 2. Ex: d - 2 = 7 3 (3) d - 2 = 7(3) 3 d - 2 = 21 +2 +2 d = 23 Here’s a tricky one! Remember to always use the sign in front of the number. DO UNDO • ÷ -7 -3 • +3 · -7 To solve for a: • First subtract 3. • Then multiply by -7. Ex: 3 - a = -2 7 • 3 - a = -2 7 -3 -3 - a = -5 7 • (-7)(- a) = (-5)(-7) 7 a = 35 Try a few on your own. • 5z + 16 = 51 • 14n - 8 = 34 • 4b + 8 = 10 -2 Example 1 5z + 16 = 51 Example 2 • 14n - 8 = 34 Example 3 • 4b + 8 = 10 -2 The answers: DO • ·5 • +16 • z=7 UNDO - 16 ÷5 DO UNDO • · 14 +8 • -8 ÷ 14 • n=3 DO • ·4 UNDO · -2 • +8 • ÷ -2 -8 ÷4 • b = -7 Consecutive Numbers • Consecutive means-- In order/In sequence. Ex: 1, 2, 3… 10,11,12… 20, 22, 24, 26… (Evens) 51, 53, 55 etc. . . (Odds) Let’s try one!!! Find three consecutive integers that have a sum of 15. What is this asking? + + = 15 Almost there! n + n+1 + n+2 = 15 • Since we don’t know what the first number is, let’s call it “n.” • The next number would be “1 more than n” • The next would be “2 more than n” Let’s complete the problem! So the problem looks like this: n + (n + 1) + (n + 2) = 15 Scary Right?!? Nah!!! 3n + 3 = 15 LIKE TERMS!!! EASY!!! Solve It!! 3n + 3 = 15 -3 -3 3n = ___ 12 ___ 3 3 n = 4 So if n = 4, (n + 1) = 5 and (n + 2) = 6 Your three consecutive numbers are: 4, 5, and 6 Assignment Algebra 1 • Pg 95 Problems 11-26 all, 29 and 33-37 odds • Honors Algebra 1 • Pg 95 Problems 11-23 odd, 25-28 all, 31-37 all 40-42 all