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

2. 11-1 Simplifying Algebraic Expressions Warm Up Simplify. 20 1.9 + 13  5 + 3 2. 16  8 + 4  1 11 3. 6 + 9  10 + 3 8 4. 17 + 8  20  2 3 Course 3

3. 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

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

5. 11-1 Simplifying Algebraic Expressions Vocabulary term like term equivalent expression simplify

6. 11-1 Simplifying Algebraic Expressions Helpful Hint Constants such as 4, 0.75, and 11 are like terms because none of them have a variable. 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.

7. 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 – 3 + 1 = 5 and 8 – 1 = 7 5y + 7

8. 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

9. 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

10. 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.

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

12. 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.

13. 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: 1 + 3 = 4 4x = 48 Divide both sides by 4. 4 4 x = 12

14. 11-1 Simplifying Algebraic Expressions Lesson Quiz Combine like terms. 1.3x + 4 + 2x2. 13k + 6  8m + 9 + k Simplify. 3. 4(3x + 6)  7x4. 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? 5x + 4 14k – 8m + 15 5x + 24 9x + 30 y = 6 $3