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

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

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

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

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

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

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

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

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

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

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

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

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