Solve Multiple Step Algebraic Equations with Variables on Both Sides MS Algebra A-REI-1 – Ch. 3.4 Multi-step Problems & Variables on Both Sides Mr. Deyo Solve Multiple Step Algebraic Equations with Variables on Both Sides

Title: 3.4 Multi-Step Problems With Variables on Both Sides Date: Learning Target By the end of the period, I will solve multi-step equations that have variables on both sides of the equal sign. I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 3.4 Pg. 149-151 3) Section ______ TxtBk. Prob. #23-31 Odd,50-54 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: How are the two images similar? How are they different? How can these two images be related to math? IMAGE 1 IMAGE 2

Daily Warm-Up Exercises For use with pages xxx–xxx A surf shop charges $85 for surfing lessons and $35 per hour to rent a surfboard. Anna paid $225. Find the number of hours she spent surfing.

Daily Warm-Up Exercises For use with pages xxx–xxx A surf shop charges $85 for surfing lessons and $35 per hour to rent a surfboard. Anna paid $225. Find the number of hours she spent surfing. ANSWER 4 hours

Vocabulary Simplest Form Equation Inverse Operations Reciprocal Distributive Property

Vocabulary Acquisition Friendly Definition Sketch Wordwork Sentence DAY 2 1. Review word Friendly Definition Physical Representation 2. Draw a sketch DAY 1 Use Visuals Introduce the word Friendly Definition Physical Representation Use Cognates Write friendly definition Word List Vocabulary Acquisition DAY 3 and/or DAY 4 1. Review the word Friendly Definition Physical Representation 2. Show how the word works Synonyms/antonym Word Problems Related words/phrases Example/non-example DAY 5 1. Review the word Friendly definition Physical Representation 3. Write a sentence at least 2 rich words (1 action) correct spelling correct punctuation correct subject/predicate agreement clear and clean writing

Whole Class Multiple Choice Practice 1 The equation is solved below. 6x – 5 = ( 16x + 60 ) 4 STEP 1 – 4x = 5 6x + 15 STEP 2 – 15 = 5 10x STEP 3 20 = 10x STEP 4 2 = x Which is the first incorrect step in the solution? Step 1 Step 2 Step 3 Step 4

Whole Class Multiple Choice Practice SOLUTION 1 The equation is solved below. 6x – 5 = ( 16x + 60 ) 4 STEP 1 – 4x = 5 6x + 15 ANSWER STEP 2 – 15 = 5 10x STEP 3 20 = 10x The correct answer is B. STEP 4 2 = x Which is the first incorrect step in the solution? Step 1 Step 2 Step 3 Step 4 In Step 2, 4x should have been subtracted from the left side of the equation instead of being added.

– 4x = 8x 7 17 Solve for the value of x. Problem A Solve an equation with variables on both sides Solve for the value of x. – 4x = 8x 7 17

x = 2 – 4x = 8x 7 17 Solve for the value of x. – 4x = 8x 7 17 – 4x = Problem A Solve an equation with variables on both sides Solve for the value of x. – 4x = 8x 7 17 – 4x = 8x 7 17 Write original equation. – 4x = 8x 7 17 + Add 8x to each side. 12x = – 17 7 Simplify each side. 12x = 24 Add 17 to each side. x = 2 Divide each side by 12. ANSWER

Problem B Solve the equation. 3 – 4a = 5(a – 3)

a = 2 3 – 4a = 5(a – 3) 3 – 4a = 5a – 15 3 = 9a – 15 18 = 9a 2 = a Problem B Solve the equation. 3 – 4a = 5(a – 3) 3 – 4a = 5a – 15 3 = 9a – 15 18 = 9a 2 = a ANSWER a = 2

CAR SALES Problem A Solve a real-world problem The annual sales report for a car dealership is shown. If these trends continue, in how many years will the number of new cars sold be twice the number of used cars sold? (-) =2

78 + 6x = ) ( 2 4x – 67 SOLUTION Problem A ANSWER Solve a real-world problem Let x represent the number of years from now. Then 6x represents the increase in the number of new cars sold over x years, and - 4x represents the decrease in the number of used cars sold over x years. Write a verbal model. 78 + 6x = ) ( 2 4x – 67 78 + 6x = 2 (67 – 4x) Write equation. 78 + 6x = 134 – 8x Distributive property 78 + 14x = 134 Add 8x to each side. 14x = 56 Subtract 78 from each side. x = 4 Divide each side by 14. ANSWER The number of new cars sold will be twice the number of used cars sold in 4 years.

Problem B WHAT IF? Suppose the car dealership sold 50 new cars this year. In how many years will the number of new cars sold be twice the number of used cars sold? (-) =2 50

6 years =2 50 WHAT IF? Problem B Suppose the car dealership sold 50 new cars this year. In how many years will the number of new cars sold be twice the number of used cars sold? (-) =2 50 ANSWER 6 years

Storm Check (Think, Write, Discuss, Report) How do you take the words of a word problem and create an equation to solve (3-4 sentences)? When I read a word problem in math, I ___________ ___________________________________________ __________________________________________.

Vocabulary Simplest Form Equation Inverse Operations Reciprocal Distributive Property

Title: 3.4 Multi-Step Problems With Variables on Both Sides Date: Learning Target By the end of the period, I will solve multi-step equations that have variables on both sides of the equal sign. I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 3.4 Pg. 149-151 3) Section ______ TxtBk. Prob. #23-31 Odd,50-54 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

Rock Climbing Ticket OUT. For $360, a rock-climbing gym offers a yearly membership where members can climb as many days as they want and pay $4 per day for equipment rental. Nonmembers pay $10 per day to use the gym and $6 per day for equipment rental. After how many visits is the total cost for a member and a nonmember the same? Turn to your partner and share your answer. Please use correct answer. Partner B, please share what Partner A told you.

V represents the number of visits Solution - Rock Climbing Ticket OUT. For $360, a rock-climbing gym offers a yearly membership where members can climb as many days as they want and pay $4 per day for equipment rental. Nonmembers pay $10 per day to use the gym and $6 per day for equipment rental. After how many visits is the total cost for a member and a nonmember the same? V represents the number of visits 360 + 4V = 10V + 6V 360 + 4V = 16V 360 = 12V 30 = V Turn to your partner and share your answer. Please use correct answer. Partner B, please share what Partner A told you.