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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions Warm Up Problem of the Day Lesson Presentation Course 3

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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions Warm Up Simplify. 5 + 3 20 2. 16 1 11 8 20 2 3 Course 3

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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions Problem of the Day Ray and Katrina are wandering through the wildlife preserve. They observe and count a total of 15 wild turkeys and deer and a total of 46 legs. How many of each did they see? 7 turkeys, 8 deer

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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions Learn to combine like terms in an expression.

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**Vocabulary 11-1 Simplifying Algebraic Expressions term like term**

equivalent expression simplify

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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions Terms in an expression are separated by plus or minus signs. Like terms can be grouped together because they have the same variable raised to the same power. Constants such as 4, 0.75, and 11 are like terms because none of them have a variable. Helpful Hint Equivalent expressions have the same value for all values of the variables.

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**Additional Example 1: Combining Like Terms To Simplify**

11-1 Simplifying Algebraic Expressions Additional Example 1: Combining Like Terms To Simplify 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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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions Check It Out: Example 1 Combine like terms. 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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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions 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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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions 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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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions 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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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions Check It Out: Example 2 Combine like terms. 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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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions To simplify an expression, perform all possible operations, including combining like terms. The Distributive Property states that a(b + c) = ab + ac for all real numbers a, b, and c. For example, 2(3 + 5) = 2(3) + 2(5). Remember!

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

11-1 Simplifying Algebraic Expressions 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 + 4n Combine coefficients 6 – 2 = 4.

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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions 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. 2c + 21 Combine coefficients 3 – 1 = 2.

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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions Additional Example 4: Combining Like Terms to Solve Algebraic Equations Solve x + 3x = 48. x + 3x = 48 Identify like terms. The coefficient of x is 1. 4x = 48 Combine coefficients: = 4 4x = 48 Divide both sides by 4. 4 4 x = 12

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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions Check It Out: Example 4 Solve 7c – c = 102. 7c – c = 102 Identify like terms. The coefficient of c is 1. 6c = 102 Combine coefficients: 7 – 1 = 6 6c = 102 Divide both sides by 6. 6 6 c = 17

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**Simplifying Algebraic Expressions**

11-1 Simplifying Algebraic Expressions Lesson Quiz Combine like terms. 1. 3x x k + 6 8m k Simplify. 3. 4(3x + 6) 7x (x + 5) + 3x Solve. 5. 6y + y = 42 6. 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 y = 6 $3

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§ 1.10 Properties of the Real Number System. Angel, Elementary Algebra, 7ed 2 Commutative Property Commutative Property of Addition If a and b represent.

§ 1.10 Properties of the Real Number System. Angel, Elementary Algebra, 7ed 2 Commutative Property Commutative Property of Addition If a and b represent.

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