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**1-6 Combining Like Terms Warm Up Problem of the Day**

Lesson Presentation Pre-Algebra

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**1-6 Combining Like Terms Warm Up Solve. 1. 9 + 13 5 + 3 20**

Pre-Algebra 1-6 Combining Like Terms Warm Up Solve. 5 + 3 20 2. 16 1 11 8 20 2 3

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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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**Learn to combine like terms in an expression.**

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Vocabulary term like term equivalent expression simplify

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**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. Equivalent expressions have the same value for all values of the variables.

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**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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**Try This: 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. A. 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. B. 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. C. 4m + 9n – 2 4m + 9n – 2 No like terms.

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**Try This: 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.**

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**Additional Example 3: Simplifying Algebraic Expressions by Combining Like Terms**

Simplify 6(5 + n) – 2n. 6(5 + n) – 2n 6(5) + 6(n) – 2n Distributive Property. 30 + 6n – 2n 6n and 2n are like terms. 30 + 4n Combine coefficients 6 – 2 = 4

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Try This: Example 3 Simplify 3(c + 7) – c. 3(c + 7) – c 3(c) + 3(7) – c Distributive Property. 3c + 21 – c 3c and c are like terms. 2c + 21 Combine coefficients 3 – 1 = 2

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**Additional Example 4: Solving Algebraic Expressions by Combining Like Terms**

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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**Try This: Example 4 Solve 7c – c = 102. 7c – c = 102 6c = 102 6c = 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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**Lesson Quiz Combine like terms. 1. 3x + 4 + 2x 2. 13k + 6 8k + 9 + 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 6k + 15 5x + 24 9x + 30 y = 6 $3

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