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

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

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

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

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

Simplifying Algebraic Expressions 11-1 Simplifying Algebraic Expressions Terms in an expression are separated by plus or minus signs. Variable: A letter used to represent a mystery number. Like terms can be grouped together because they have the same variable raised to the same power. Constant: A number without a variable. All constants can be combined because they are like terms. Coefficient: The number in front of a variable. This number is being multiplied by the variable.

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 – 3 + 1 = 5 and 8 – 1 = 7 5y + 7

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

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

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.

Simplifying Algebraic Expressions 11-1 Simplifying Algebraic Expressions 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).

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) + 6(n) – 2n Distributive Property. 30 + 6n – 2n Multiply. 30 + 4n Combine like terms. 6 – 2 = 4.

Additional Example 3: Using the Distributive Property to Simplify 11-1 Simplifying Algebraic Expressions Additional Example 3: Using the Distributive Property to Simplify Simplify 5(3 + 2n) – n. 5(3) + 5(2n) – n Distributive Property. 15 + 10n – n Multiply. 15 + 9n Combine like terms

Additional Example 3: Using the Distributive Property to Simplify 11-1 Simplifying Algebraic Expressions Additional Example 3: Using the Distributive Property to Simplify Simplify 5(6 – 5x) + 10. 5(6) - 5(5x) + 10 Distributive Property. 30 – 25x + 10 Multiply. Combine like terms 40 – 25x

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

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

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

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