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Preview Warm Up California Standards Lesson Presentation

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Warm Up Simplify. 5 + 3 20 2. 16 1 11 8 20 2 3

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AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g. identity, inverse, distributive, associative, commutative) and justify the process used. California Standards

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Vocabulary term like term coefficient constant equivalent expression

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**In the expression below, 7x, 5, 3y, and 2x are terms**

In the expression below, 7x, 5, 3y, and 2x are terms. A term can be a number, a variable, or a product of numbers and variables. Terms in an expression are separated by plus or minus signs. Constant Coefficients

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Like terms, such as 7x and 2x, can be grouped together because they have the same variable raised to the same power. Often, like terms have different coefficients. A coefficient is a number that is multiplied by a variable in an algebraic expression. A constant is a number that does not change. Constants, such as 4, 0.75, and 11, are also like terms. When you combine like terms, you change the way an expression looks but not the value of the expression. Equivalent expressions have the same value for all values of the variables.

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**Additional Example 1: Combining Like Terms in One-Variable Expressions**

Combine like terms. A. 14a – 5a Identify like terms. 9a Combine coefficients: 14 – 5 = 9 Identify like terms; the coefficient of y is 1, because 1y = y. B. 7y + 8 – 3y – 1 + y Combine coefficients: 7 – = 5 and 8 – 1 = 7 5y + 7

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**When you rearrange terms, move the operation in front of each term with that term.**

Helpful Hint

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**Check It Out! Example 1 Combine like terms. A. 4q – q 3q**

Identify like terms; the coefficient of q is 1, because 1q = q. A. 4q – q 3q Combine coefficients: 4 – 1 = 3 Identify like terms; the coefficient of c is 1, because 1c = c. B. 5c + 8 – 4c – 2 – c Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6 6

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**Additional Example 2A: Combining Like Terms in Two-Variables Expressions**

Combine like terms. 9x + 3y – 2x + 5 9x + 3y – 2x + 5 Identify like terms. 7x + 3y + 5 Combine coefficients: 9 – 2 = 7

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**Additional Example 2B: Combining Like Terms in Two-Variable Expressions**

Combine like terms. 5t + 7p – 3p – 2t 5t + 7p – 3p – 2t Identify like terms. Combine coefficients: 5 – 2 = 3 and 7 – 3 = 4 3t + 4p

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**Additional Example 2C: Combining Like Terms in Two-Variable Expressions**

Combine like terms. 4m + 9n – 2 4m + 9n – 2 No like terms.

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**Check It Out! Example 2 Combine like terms. 2x + 5x – 4y + 3**

A. 2x + 5x – 4y + 3 2x + 5x – 4y + 3 Identify like terms. 7x – 4y + 3 Combine coefficients: = 7 B. 9d + 7c – 4d – 2c 9d + 7c – 4d – 2c Identify like terms. 5d + 5c Combine coefficients: 9 – 4 = 5 and 7 – 2 = 5 C. 8g + c – 6 8g + c – 6 No like terms.

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To simplify an expression, perform all possible operations, including combining like terms. You may need to use the Associative, Commutative, or Distributive Properties.

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**Additional Example 3: Using the Distributive Property to Simplify**

Simplify 6(5 + n) – 2n. 6(5 + n) – 2n 6(5) + 6(n) – 2n Distributive Property 30 + 6n – 2n Multiply. 30 + 6n – 2n Identify like terms. 30 + 4n Combine coefficients: 6 – 2 = 4.

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Check It Out! Example 3 Simplify 3(c + 7) – c. 3(c + 7) – c 3(c) + 3(7) – c Distributive Property 3c + 21 – c Multiply. 3c + 21 – c Identify like terms. 2c + 21 Combine coefficients: 3 – 1 = 2.

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**Lesson Quiz Combine like terms. 1. 3x + 4 + 2x 2. 13k + 6 8m + 9 + k**

Simplify. 3. 4(3x + 6) 7x (x + 5) + 3x Solve. 5. The accounting department ordered 15 boxes of pens. The marketing department ordered 9 boxes of pens. If the total cost of the combined order was $72, what is the price of each box of pens? 5x + 4 14k – 8m + 15 5x + 24 9x + 30 $3

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