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Distributive Property, Combining Like Terms, Solving Equations with Variables on Both Sides

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Distributive Property An algebra property which is used to multiply a single term and two or more terms inside a set of parentheses. An algebra property which is used to multiply a single term and two or more terms inside a set of parentheses. 2 (3 + 6)

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6(2+4x) The two terms inside the parentheses cannot be added because they are not like terms. Therefore, 2 + 4x, the expression inside the parentheses, cannot be simplified any further. The two terms inside the parentheses cannot be added because they are not like terms. Therefore, 2 + 4x, the expression inside the parentheses, cannot be simplified any further. Therefore, we must distribute the 6 across the parentheses! Therefore, we must distribute the 6 across the parentheses!

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-(3 + x2) Change each positive or negative sign of the terms that were inside the parentheses. Negative or minus signs become positive or plus signs. Change each positive or negative sign of the terms that were inside the parentheses. Negative or minus signs become positive or plus signs.

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Try Some Yourself! 9(x + 9) 9(x + 9) 2(4 + 9x) 2(4 + 9x) 7(x + -1) 7(x + -1) 12(a + b + c) 12(a + b + c) -10( x) -10( x)

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Combining Like Terms Term Term Number, variable, or product/quotient of numbers and variables (Ex: 5, m, 2x ²) Number, variable, or product/quotient of numbers and variables (Ex: 5, m, 2x ²) Like Terms Like Terms Terms with the same variable AND exponent Terms with the same variable AND exponent

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Combining Like Terms To simplify expressions with like terms, add or subtract the coefficients. To simplify expressions with like terms, add or subtract the coefficients. 4k + 5k = 9k

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Combining Like Terms 2ab + 6ba 2ab + 6ba Can you add the following? Can you add the following? 3x ³y + 2xy³

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Try It Yourself! 1) -x + 3y – 2x + y x -1 2) 5a – 3b + 12 – a + 3 – 14b 3) 3x + 2m – 14x + 2x – 4m

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Solving Equations with Variables on Both Sides If you had this equation, how would you move the 7 to the other side of the equation? If you had this equation, how would you move the 7 to the other side of the equation? 3x + 3 = x + 7

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How would you move the x from the left side to the right side? How would you move the x from the left side to the right side? 3x + 3 = x + 7 Exactly the same way you moved the seven!

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Once you subtract the x from both sides, the equation becomes a two-step equation! Once you subtract the x from both sides, the equation becomes a two-step equation! 2x + 3 = 7

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Try This One on Your Own! 4x + 7 = 2x -1

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Another One! -2x – 10 = -9x + 11

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