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M1A U1D4 Warm Up: Write each phrase as an algebraic expression. 1.$5 less than the original price. 2.9 more than 7 multiplied by g. 3.7 times the product of 15 and y. 4.22 less the quantity d and 35.

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Warm Up: Write each phrase as an algebraic expression. 1.$5 less than the original price. p - 5 2.9 more than 7 multiplied by g. 7g + 9 3.7 times the product of 15 and y. 7(15y) 4.22 less the quantity d and 35. 22-35d

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Homework Check: Go over HW

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Objective: Students will be able to: Solve multi-step equations using the Distributive Property. Have an understanding of what property is used when solving equations.

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Properties... Review the basic properties used in mathematics. Just watch…there’s a handout coming!

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Commutative Property: The order in which numbers are added or multiplied does not change the sum or product. a +b = b +a and a ∙b = b ∙a

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Associative Property: The way in which numbers are grouped when added or multiplied does not change the sum or product. (a +b) + c = a +(b+c) and (a ∙b) ∙c = a ∙(b ∙c)

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Additive and Multiplicative Inverses: For every a, there is an inverse (opposite operation). a +(-a) = (a +-a) = 0 and a ∙ (1/a) = (1/a) ∙a = 1

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Distributive Property: For any numbers a, b, and c: a(b+c) = ab + ac and (b+c)a = ba + ca a(b-c) = ab - ac and (b-c)a = ba - ca Distribute Handout

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Steps to Solving Multi-Step Equations: 1.Distribute to clear parenthesis. 2.Combine like terms. 3.Use addition/subtraction to get the variables on one side. 4.Add or subtract to isolate the variable. 5.Multiply or divide to isolate the variable.

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Distribute Notes on Multi-Step Equations – Special Cases Complete together!

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Additional Examples Example 1: Equations have one solution when the variables do not cancel out. For example, 10x – 23 = 29 – 3x +3x +3x 13x - 23 = 29 +23 +23 13x = 52 13 13 x = 4

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Example 2: Equations with no solution have variables that will cancel out and constants that are not equal. For example, -x + 7 – 6x = 19 – 7x -7x + 7 = 19 – 7x +7x 7 ≠19 False therefore no solution!

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Example 3: An equation with infinitely many solutions occurs when variables cancel out and constants are equal. For example, -1/2 (36a – 6) = ¾ (4 – 24a) -18a + 3 = 3 – 18a +18a +18a 3 = 3 True therefore infinite solutions!

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Additional Examples Example 4: A special equation with one solution when the variables do not cancel out. 5x + 29 = 29 – 3x +3x +3x 8x + 29 = 29 -29 -29 8x = 0 8 8 x = 0

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Classwork: Solving Multi-step Equations Special Cases #1-6 Handout

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CW 2 : Solving Multi-Step Equations with Distributive Property #1-6

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Homework: Kuta Multi-Step Equations EVENS

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