1. Simplifying Algebraic Expressions 11-1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. Simplifying Algebraic Expressions 11-1 Warm Up Simplify. 20 11 8 3 4. 17 + 8  20  2 3. 6 + 9  10 + 3 2. 16  8 + 4  1 1. 9 + 13  5 + 3

3. Simplifying Algebraic Expressions 11-1 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

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

5. Simplifying Algebraic Expressions 11-1 Vocabulary terms like terms equivalent expressions simplify

6. Simplifying Algebraic Expressions 11-1 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 exponents. Equivalent expressions have the same value for all values of the variables. Constants such as 4, 0.75, and 11 are like terms because none of them have a variable. Helpful Hint

7. Simplifying Algebraic Expressions 11-1 To simplify an expression, perform all possible operations, including combining like terms.

8. Simplifying Algebraic Expressions 11-1 Combine like terms. Additional Example 1: Combining Like Terms To Simplify Identify like terms. Combine coefficients: 14 – 5 = 9 A. 14a – 5a 9a9a B. 7y 2 + 8 – 3y 2 – 1 + y Identify like terms; the coefficient of y is 1, because 1y = y. Combine coefficients: 7 – 3 = 4 and 8 – 1 = 7 4y 2 + y + 7

9. Simplifying Algebraic Expressions 11-1 Combine like terms. Check It Out: Example 1 Identify like terms; the coefficient of q is 1, because 1q = q. Combine coefficients: 4 – 1 = 3 Identify like terms; the coefficient of c is 1, because 1c = c. Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6 6 3q3q A. 4q – q B. 5c + 8 – 4c – 2 – c

10. Simplifying Algebraic Expressions 11-1 Combine like terms. Additional Example 2A: Combining Like Terms in Two-Variables Expressions Identify like terms. Combine coefficients. 5t 2 + 7p – 3p – 2t 2 3t 2 + 4p 5t 2 + 7p – 3p – 2t 2

11. Simplifying Algebraic Expressions 11-1 Combine like terms. Additional Example 2B: Combining Like Terms in Two-Variable Expressions No like terms. 4m 3 + 9n – 2

12. Simplifying Algebraic Expressions 11-1 Combine like terms. Check It Out: Example 2 Identify like terms. Combine coefficients. A. 2x + 5x – 4y + 3 7x – 4y + 3 2x + 5x – 4y + 3 Identify like terms. Combine coefficients. B. 9d + 7c – 4d – 2c 5d + 5c 9d + 7c – 4d – 2c No like terms. C. 8g + c – 6 8g + c – 6

13. Simplifying Algebraic Expressions 11-1 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!

14. Simplifying Algebraic Expressions 11-1 Simplify 6(5 + n) – 2n. Additional Example 3: Using the Distributive Property to Simplify Distributive Property. Multiply. 6(5 + n) – 2n 30 + 6n – 2n 6(5) + 6(n) – 2n 30 + 4n Combine coefficients: 6 – 2 = 4.

15. Simplifying Algebraic Expressions 11-1 Simplify 3(c + 7) – c. Check It Out: Example 3 Distributive Property. Multiply. 3(c + 7) – c 3c + 21 – c 3(c) + 3(7) – c 2c + 21 Combine coefficients: 3 – 1 = 2.

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

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

18. Simplifying Algebraic Expressions 11-1 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

19. Simplifying Algebraic Expressions 11-1 Lesson Quiz Combine like terms. 1. 3x 2 + 4 + 2x 2 2. 13k + 6 – 8m + 9 + k Simplify. 3. 4(3x + 6) – 7x 4. 6(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? 14k – 8m + 15 y = 6 5x 2 + 4 5x + 249x + 30 $3

20. Simplifying Algebraic Expressions 11-1 1. Combine like terms. 4p + 13 + 11p A. 15p 2 + 13 B. 15p + 13 C. 28p D. 28 Lesson Quiz for Student Response Systems

21. Simplifying Algebraic Expressions 11-1 2. Combine like terms. 15t + 9 – 7s + 10 + 5t A. 15t – 7s – 1 B. 15t – 7s + 1 C. 20t – 7s + 19 D. 20t + 7s + 19 Lesson Quiz for Student Response Systems

22. Simplifying Algebraic Expressions 11-1 3. Simplify 7(4m + 9) – 9m. A. 19m + 9 B. 19m + 63 C. 37m + 9 D. 37m + 63 Lesson Quiz for Student Response Systems

23. Simplifying Algebraic Expressions 11-1 4. Solve 11v + 2v = 65. A. v = 2 B. v = 5 C. v = 7 D. v = 11 Lesson Quiz for Student Response Systems