Simplify. Warm-Up Exercises ANSWER () 22 ( ),), 16 $98 ANSWER 15x3 – ANSWER 16 6y 26y () 5x3 – 2. () 4+6 y 2y 2 8 – You bought 3 DVDs for $22 each and 2 CDs for $16 each. Write and simplify an expression for the total cost. 3.

Identify Terms in an Expression Example 1 Identify the terms in the expression. 11 – 2x 2 – 7x7x – 11 – 2x 2 – 7x7x – = 11 – () 7x7x – 2x 2 – () ++ ANSWER The terms of the expression are. 11, – 2x 2 – 7x, and – Write the expression as a sum. SOLUTION

Identify Coefficients and Like Terms Example 2 Identify the coefficients and like terms in the expression. – x 2 7x7x–+53x 2 –10– Begin by writing the expression as a sum in order to identify the terms. SOLUTION x 2 7x7x–+53x 2 –10– () – 3x 2 – () x 2 +5 () 7x7x – +++ = ANSWER The coefficients of the expression are 1, 7, and 3. The terms x 2 and 3x 2 are like terms. The terms 5 and 10 are also like terms. –– – –

Identify the terms, coefficients, and like terms in the expression Checkpoint 4x 3 9x9x–+5x 2 –x 2 9x 3 7x.7x. –+ Identify Terms, Coefficients, and Like Terms ANSWER terms: 4x 3, 5x 2, x 2, 9x, 9x 3, 7x ; ––– like terms: 4x 3 and 9x 3, 5x 2 and x 2, 9x and 7x ––– coefficients: 4, 5, 1, 9, 9, 7 ; ––– 1.

Example 3 Simplify by Combining Like Terms Simplify the expression. 9x9x+5x5x a. 2x22x2 + – 3x3xx2x2 + 6x6x b. 7x7x4y4y c. –– 3x3x+12y Add. 14x = SOLUTION 9x9x+5x5x a. () 9+5x = Distributive property

Example 3 Simplify by Combining Like Terms Distributive property 2 + – xx2x2 + 3 ()() = 16 9x9xx2x2 + = Add or subtract. 7x7x4y4y c. –– 3x3x + 12y 4y4y ( ) = – 7x7x ++ 3x3x ( )– Group like terms. 4 ( ) = – ( )– y x Distributive property = – 8y8y – 4x4x Add or subtract. 2x22x2 + – 6x6xx2x2 + 3x3x ()() Group like terms. 2x22x2 + – 3x3xx2x2 + 6x6x b. =

Example 4 Simplify Expressions with Grouping Symbols Simplify the expression. b. 512 a. – – () 1x 4 – () x6 3 – () 8x + Group like terms. – +5x5x = () 5+12 Add. – +5x5x = 17 SOLUTION 512 a. – – () 1x – 5+5x5x = 12 Distributive property

Example 4 Simplify Expressions with Grouping Symbols = Group like terms. () 4x4x – 3x3x+ () + – 24 = Distributive property () 4 – 3+ () + – 24 x = Add or subtract. x – b. 4 – () x6 3 – () 8x + – 4x4x24 3x3x – + = Distributive property

Checkpoint 2. ANSWER 4x4x 3x3x7x7x– 3. x1+ 810x – + ANSWER 711x– 4. x + x2x2 – 4x24x2 – 5x5x ANSWER – 3x23x2 – 4x4x Simplify the expression () 4+x2 ANSWER 11+2x2x 6. x () 2x6 –– ANSWER – 5x5x + 12 Simplify Expressions

Checkpoint Simplify the expression. 7. () 1x3 – ANSWER 2x2x + 6 – () 9x – Simplify Expressions

Example 5 Use a Real-Life Model Rowboat Rentals A boat rental company charges customers for rowboats as shown in the advertisement. There is a 1 hour minimum rental time. a.Write and simplify an expression that gives the total cost to rent a rowboat for h hours, where. 1h ≥ b. Find the total cost of renting a rowboat for 8 hours.

Example 5 Use a Real-Life Model (dollars per hour) LABELSCost for first hour 13 = (dollars) Cost for each additional hour 6 = Number of additional hours = (hours) 1 h– SOLUTION VERBAL MODEL Cost for first hour Number of additional hours a. Cost for each additional hour +

Example 5 Use a Real-Life Model ALGEBRAIC MODEL = 13+ () 16 h– + 66h6h – = + 66h6h – = 7+ 6h6h ANSWER The total cost of renting a rowboat for 1 hour or longer is given by the expression. 76h6h + b. To find the total cost of renting a rowboat for 8 hours, evaluate the expression for. 8h = 76h6h + Substitute 8 for h. = 7 + () 86

Example 5 Use a Real-Life Model Multiply. = Add. = 55 ANSWER Renting a rowboat for 8 hours will cost $55.

Checkpoint A calling card charges $1 for all phone calls up to 15 minutes and $.25 for each additional minute. 8. Write and simplify an expression that gives the total cost of a phone call that lasts m minutes, where m is at least 15. ANSWER, or 1+ () m– m– 9. Use your answer from Exercise 8 to find the total cost of a phone call that lasts for 28 minutes. ANSWER $4.25 Use a Real-Life Model

Checkpoint A calling card charges $1 for all phone calls up to 15 minutes and $.25 for each additional minute. 10. Use your answer from Exercise 8 to find the total cost of a phone call that lasts for 1 hour 10 minutes. ANSWER $14.75 Use a Real-Life Model