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LESSON – ALGEBRAIC EXPRESSIONS [TEXT: LESSON 1-3] ALGEBRAIC EXPRESSION – A mathematical statement that contains one or more variables Examples: 3n + 8, 3(2x + 5), Examples/Practice: Write an algebraic expression that models each situation. Use the algebraic expression to answer each set of questions. 1) You have $150, but you are spending $2 each day for school lunch. Write an algebraic expression to represent the amount of money you will have remaining after d days. 2) Joe has $100. He earns $12 an hour. Write an algebraic expression to model the amount of of money Joe has after working x hours. a) How much money will you have after 17 days? a) How much money will Joe have after working a 40 hour week? b) How much money will you have after 45 days? b) How much money will Joe have after working 15 hours? c) In how many days will you have no money left? c) Joe has been saving to purchase a new laptop computer that costs $1450. How many hours must he work to have enough money to purchase computer? Examples: Write an algebraic expression that models the given word phrase. 3) 4 more than twice a number n 4) sum of numbers a and b divided by 2 5) half the difference of a number n and 5 6) quotient of the sum of a number x and 5 and twice the number y EVALUATE AN ALGEBRAIC EXPRESSION – To evaluate an algebraic expression, substitute a number for each variable in the expression. Then simplify using the order of operations. Examples: Evaluate each algebraic expression for the given values of the variable. 8) 2x3 – 5x for x = 3 9) for a = 9 and b = –2 10) for x = 7 and y = 4 ASSIGNMENT LESSON 1-3: ALGEBRAIC EXPRESSIONS For 1 & 2: Write an algebraic expression that models each situation. Use the algebraic expression to answer each set of questions. 1) A water storage tank contains 240 gallons of water. Each day the tank loses 2.5 gallons of water due to a small pin hole leak at the bottom of the tank. Write an algebraic expression that models the amount of water remaining in the tank after d days have passed. 2) A small swimming pool is being filled with water. Initially, the pool contained 3000 gallons of water. Water is being pumped into the pool at a rate of 10 gallons per minute. Write an algebraic expression that models the amount of water in the pool after m minutes. a) How much water remains in the tank after 40 days? a) How much water is in the pool after 110 minutes of pumping water into the pool? b) How much water remains in the tank after 100 days? b) How much water is in the pool after 4 hours of pumping water into the pool? c) In how many days will the tank be empty? c) When full the pool contains approximately 7000 gallons. How many minutes will it take to fill the pool? For 3-6: Write an algebraic expression that models the given word phrase. 3) seven fewer than twice a number n 4) two times the sum of a and b 5) nine more than the product of 5 and a number x 6) quotient of 4 more than the number x and the number y decreased by 3 For 7-10: Evaluate each algebraic expression for the given values of the variable. 7) 7(a + 4) + 3b – 8 for a = –4 and b = 5 9) for x = 6 and y = –3 8) 3x2 – 5x + 2 10) for x = –2 + y2 for x = –8 and y = 5 ALGEBRA 2 WARM-UPS (After Lesson 1-3) 1) Suzzanah walks after school each day. 2) The Siuslaw Booster Club is having a She has walked a total of 35 miles and plans membership drive. They currently have 25 to continue to walk 3 miles each day thereafter. members and have a goal of recruiting 5 new Write an algebraic expression that models members per week. Write an algebraic expression the distance traveled after d days. that models the total number of members after w weeks of recruitment. a) How far (total) will she have walked after 14 days? 6 weeks? a) How many members do they hope to have in 10 weeks? 25 weeks? b) How many days will she have to walk to reach a total of 200 miles? b) If the club’s goal is to have at least 200 members, in how many weeks will they reach this goal?