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Chapter 3 Lesson 5 Solving 2-Step Equations Pgs. 120-124 What you will learn: To solve 2-step equations!

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Background A two step equation contains two operations. In the equation 2x + 1 = 9, x is multiplied by 2 and then 1 is added. To solve two-step equations, use inverse operations to undo each operation in reverse order. You can solve 2x + 1 = 9 in two steps. Step 1: First, undo addition 2x + 1 = 9 2x + 1 -1 = 9 -1 Subtract 1 from each side 2x = 8 Step 2: Undo the multiplication 2x = 8 2 2x = 4

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How do you do the check of 2x + 1 = 9 if x = 4? Replace the x with 4 in the ORIGINAL Problem and solve step by step. 2(4) + 1 = 9 8 + 1 = 9 9 = 9 This problem checks out!

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Solve a two-step equation and check the solution. 5x - 2 = 13 Step 1: Undo the subtraction. 5x - 2 +2 = 13 +2 5x = 15 Step 2: Undo the multiplication 5x = 15 5 5 x = 3 Check: 5x - 2 = 13 5(3) - 2 = 13 15 - 2 = 13 13 = 13

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Solve the equation and check the answer. 4 = n + 11 6 What do you do first? Undo the addition 4 - 11 = n + 11 -11 6 -7 = n 6 What do you do next? Undo the division -7(6) = n (6) 6 -42 = n

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Now check your answer In the original problem. 4 = n + 11 6 4 = -42 + 11 6 4 = -7 + 11 4 = 4 Remember, in order for a check to work out, both sides of the equation need to equal the same!!

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Solve an equation with Negative coefficients 4 - x = 10 Think of the problem as 4 - 1x = 10 4 - 4 - 1x = 10 - 4 -1x = 6 -1 -1 x = -6 Check: 4 - x = 10 4 - (-6) = 10 10 = 10

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Combine Like Terms before solving m - 5m + 3 = 47 Remember it can be rewritten as m + (-5m) + 3 = 47 Combine like terms: m - 5m + 3 = 47 -4m + 3 = 47 Subtract 3 from each side: -4m + 3 - 3 = 47 - 3 Simplify: -4m = 44 Divide both sides by -4: -4m = 44 -4 -4 Simplify: m = -11 Check: m - 5m + 3 = 47 -11 - 5(-11) + 3 = 47 -11 + 55 + 3 = 47 44 + 3 = 47 47 = 47

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Use an equation to solve a problem A telephone calling card allows for 25¢ per minute plus a one-time service charge of 75 ¢. If the total cost of the card is $5, solve 25m + 75 = 500 to find the number of minutes you can use the card. Step 1: Undo the addition 25m + 75 -75 = 500 -75 25m = 425 Step 2: Undo the multiplication 25m = 425 25 m = 17 Check: 25(17) + 75 = 500 425 + 75 = 500 500 = 500

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You try. Look at the questions Carefully! 3y + 4 = 13 20 - z = 11 3n + n - 4 = 12 3y + 4 -4 = 13 - 4 3y = 9 3y = 9 y = 3 3 3 20 - 20 - z = 11 - 20 -z = -9 -1 -1 z = 9 4n - 4 + 4 = 12 + 4 4n= 16 4 4 n = 4 Check: 3(3) + 4 = 13 9 + 4 = 13 13 = 13 20 - 9 = 11 11 = 11 3(4) + 4 - 4 = 12 12 = 12

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