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Two-Step Equations 33 22 11 Review 1-Step 2-Step Equations Practice Problems

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Review: ONE STEP EQUATIONS

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ONE STEP EQUATIONS What you do to one side of the equation must also be done to the other side to keep it balanced. An equation is like a balance scale because it shows that two quantities are equal.

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ONE STEP EQUATIONS What is the variable? To solve one step equations, you need to ask three questions about the equation: What operation is performed on the variable? What operation is performed on the variable? What is the inverse operation? What is the inverse operation? (The one that will undo what is being done to the variable)

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ONE STEP EQUATIONS Example 1 Solve x + 4 = 12 What is the variable? Using the subtraction property of equality, subtract 4 from both sides of the equation. - 4 - 4 x x + 4 = 12 x + 4 = 12 The variable is x. Addition. Subtraction. What is the inverse operation (the one that will undo what is being done to the variable)? What operation is being performed on the variable? - 4 8= The subtraction property of equality tells us to subtract the same thing on both sides to keep the equation equal.

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ONE STEP EQUATIONS Example 2 Solve y - 7 = -13 What is the variable? Using the addition property of equality, add 7 to both sides of the equation. y - 7 = -13 + 7 + 7 y The variable is y. Subtraction. Addition. What operation is being performed on the variable? What is the inverse operation (the one that will undo what is being done to the variable)? + 7 =-6 The addition property of equality tells us to add the same thing on both sides to keep the equation equal.

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ONE STEP EQUATIONS Example 3 Solve –6a = 12 What is the variable? Using the division property of equality, divide both sides of the equation by –6. –6a = 12 -6 a The variable is a. What operation is being performed on the variable? Multiplication. What is the inverse operation (the one that will undo what is being done to the variable)? Division -6 =-2 The division property of equality tells us to divide the same thing on both sides to keep the equation equal.

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ONE STEP EQUATIONS Example 4 Solve What is the variable? Using the multiplication property of equality, multiply both sides of the equation by 2. = -10 b The variable is b. What operation is being performed on the variable? Division. What is the inverse operation (the one that will undo what is being done to the variable)? Multiplication = -10 = -10 2 2 =-20 =-10 The multiplication property of equality tells us to multiply the same thing on both sides to keep the equation equal.

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Solving Two-Step Equations

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What is a Two-Step Equation? An equation written in the form Ax + B = C

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Examples of Two-Step Equations a) 3x – 5 = 16 b) y/4 + 3 = 12 c) 5n + 4 = 6 d) n/2 – 6 = 4

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Steps for Solving Two-Step Equations 1. Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both sides of the equation. 2. Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of the equation.

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Opposite Operations Addition Subtraction Multiplication Division

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Helpful Hints? Identify what operations are on the variable side. (Add, Sub, Mult, Div) “Undo” the operation by using opposite operations. Whatever you do to one side, you must do to the other side to keep equation balanced.

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Ex. 1: Solve 4x – 5 = 11 4x – 5 = 15 +5 +5(Add 5 to both sides) 4x = 20(Simplify) 4 4(Divide both sides by 4) x = 5(Simplify)

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Try These Examples 1. 2x – 5 = 17 2. 3y + 7 = 25 3. 5n – 2 = 38 4. 12b + 4 = 28

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Check your answers!!! 1. x = 11 2. y = 6 3. n = 8 4. b = 2

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Ready to Move on?

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Ex. 2: Solve x/3 + 4 = 9 x/3 + 4 = 9 - 4 - 4 (Subt. 4 from both sides) x/3 = 5 (Simplify) (x/3) 3 = 5 3 (Mult. by 3 on both sides) x = 15 (Simplify)

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Try these examples! 1. x/5 – 3 = 8 2. c/7 + 4 = 9 3. r/3 – 6 = 2 4. d/9 + 4 = 5

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Check your answers!!! 1. x = 55 2. c = 35 3. r = 24 4. d = 9

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