11 1 Simplifying Algebraic Expressions Warm Up Problem

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

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

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

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

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. Helpful Hint Equivalent expressions same Constants such as 4, 0. 75, have and the 11 are like value all values ofof the variables. termsfor because none them have a variable.

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

11 -1 Simplifying Algebraic Expressions Additional Example 2 A: Combining Like Terms in Two -Variables Expressions Combine like terms. 9 x + 3 y – 2 x + 5 Identify like terms. 7 x + 3 y + 5 Combine coefficients: 9 – 2 = 7

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

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

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

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

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

11 -1 Simplifying Algebraic Expressions Lesson Quiz Combine like terms. 1. 3 x + 4 + 2 x 5 x + 4 Simplify. 2. 13 k + 6 8 m + 9 + k 14 k – 8 m + 15 3. 4(3 x + 6) 7 x 5 x + 24 4. 6(x + 5) + 3 x 9 x + 30 Solve. 5. 6 y + y = 42 y = 6 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? $3