1-6 Combining Like Terms Warm Up Problem of the Day Lesson Presentation Pre-Algebra

1-6 Combining Like Terms Warm Up Solve. 1. 9 + 13  5 + 3 20 Pre-Algebra 1-6 Combining Like Terms Warm Up Solve. 1. 9 + 13  5 + 3 20 2. 16  8 + 4  1 11 3. 6 + 9  10 + 3 8 4. 17 + 8  20  2 3

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

Learn to combine like terms in an expression.

Vocabulary term like term equivalent expression simplify

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.

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

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

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

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

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

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: 2 + 5 = 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.

To simplify an expression, perform all possible operations, including combining like terms.

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

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

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

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

Lesson Quiz Combine like terms. 1. 3x + 4 + 2x 2. 13k + 6  8k + 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 6k + 15 5x + 24 9x + 30 y = 6 $3