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ESSENTIAL SKILLS: SOLVE EQUATIONS BY USING ADDITION AND SUBTRACTION SOLVE EQUATIONS BY USING MULTIPLICATION AND DIVISION 2-2: Solving One-Step Equations

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Addition Property of Equality If an equation is true and the same number is added to each side of the equation, the resulting equivalent equation is also true. Examples 14 = 14-3 = -3 14 + 3 = 14 + 3+9 +9 17 = 17 6 = 6

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2-2: Solving One-Step Equations Example 1 Solve h – 12 = -27. Then check your solution. h – 12 = -27Original Equation h – 12 + 12 = -27 + 12Add 12 to each side h = -15Simplify To check, substitute -15 back in the original equation (-15) – 12 = -27 -27 = -27

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1) Solve a – 24 = 16 1. 40 2. -8 3. 8 4. -40

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2-2: Solving One-Step Equations Subtraction Property of Equality If an equation is true and the same number is subtracted from each side of the equation, the resulting equivalent equation is also true. Examples 87 = 87 13 = 13 87 – 17 = 87 – 17-28 -28 70 = 70-15 = -15

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2-2: Solving One-Step Equations Example 2 Solve c + 102 = 36. Then check your solution. c + 102 = 36Original Equation c + 102 – 102 = 36 – 102 Add 12 to each side c = -66Simplify To check, substitute -66 back in the original equation (-66) + 102 = 36 36 = 36

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2) Solve 129 + x = -42 1. 87 2. -171 3. 171 4. -87

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2-2: Solving One-Step Equations Multiplication Property of Equality If an equation is true and each side is multiplied by the same nonzero number, the resulting equivalent equation is also true. Example If x = 5, then 3x = 15 Division Property of Equality If an equation is true and each side is divided by the same nonzero number, the resulting equivalent equation is also true. Example If x = -20, then x / 5 = -20 / 5 = -4

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2-2: Solving One-Step Equations Example 3A Solve (-1 3 / 8 )k = 2 / 3 (-1 3 / 8 )k = 2 / 3 Original Equation (- 11 / 8 )k = 2 / 3 Convert to an improper fraction (- 8 / 11 )(- 11 / 8 )k = (- 8 / 11 ) 2 / 3 Multiply each side by - 8 / 11, the reciprocal k = - 16 / 33 of - 11 / 8 Example 3B Solve -75 = -15b -75 = -15bOriginal Equation -15 -15Divide each side by -15 5 = bSimplify

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3) Solve (4 1 / 3 )m = 5 3 / 7 1. 114 / 91 2. 44 / 7 3. 23 / 21 4. 5

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4) Solve 32 = -14c 1. -3 2. 46 3. 18 4. - 16 / 7

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2-2: Solving One-Step Equations Assignment Page 86 1 – 61, odds Skip #17 & #43 Must show work for credit

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