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**The Distributive Property**

Lesson 3 Linear Equations The Distributive Property

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**Warm-Up State whether the equation is true or not with the**

given values. 6x – 4y = 22 when x = 5 and y = 2 x + 5 = y when x = 6 and y = 11 y = – 3x – 1 when x = – 2 and y = – 7

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**The Distributive Property**

Target: Simplify expressions using the Distributive Property and combining like terms.

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**Vocabulary Term: A number or the product of a number and a variable.**

Constant: Term that has no variable. Coefficient: The number multiplied by a variable in a term. Distributive Property: A property that can be used to rewrite an expression without parentheses. Like Terms: Terms that have the same variable raised to the same power. Equivalent Expressions: Expressions that have the same value.

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**The Distributive Property**

For any numbers a, b and c: a(b + c) = a ∙ b + a ∙ c a(b – c) = a ∙ b – a ∙ c

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Example 1a Use the Distributive Property to simplify each expression. 2(x + 6) 2(x) + 2(6) 2x + 12

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Example 1b Use the Distributive Property to simplify each expression.

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Example 1c Use the Distributive Property to simplify each expression. – 5(3x – 1) – 5(3x) – (– 5)(1) – 15x + 5

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Example 2a Find the product by using the Distributive Property and mental math. 4(103) 4( ) 4(100) + 4(3)

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Example 2b Find the product by using the Distributive Property and mental math. 998 ∙ 7 7(1000 – 2) 7(1000) – 7(2) 7000 –

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Example 2c Find the product by using the Distributive Property and mental math. 8(6.5) 8( ) 8(6) + 8(0.5)

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Example 3 Simplify by combining like terms. 3x – 2y + 4 – 2x + x + 4y 2x + 2y + 4

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Example 4 Simplify by combining like terms – 5(2x – 1) + 3x – 2 – 10x x – 2 – 7x + 3

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**Exit Problems Simplify each expression. 4(x − 3) 9x + 2 + 3x – 4 − 7x**

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Communication Prompt How could the Distributive Property help you do mental math in real-world situations?

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