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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. 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. 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.

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

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**Combining Like Terms Term**

Number, variable, or product/quotient of numbers and variables (Ex: 5, m, 2x²) Like Terms 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. 4k + 5k = 9k

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Combining Like Terms 2ab + 6ba Can you add the following? 3x³y + 2xy³

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**Try It Yourself! -x + 3y – 2x + y + 4 + 5x -1**

5a – 3b + 12 – a + 3 – 14b 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? 3x + 3 = x + 7

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**Exactly the same way you moved the seven!**

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!**

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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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In this lesson, you will be shown how to combine like terms along with using the distributive property.

In this lesson, you will be shown how to combine like terms along with using the distributive property.

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