MS Algebra A-REI-3 – Ch. 4.3 Multi-Step Inequalities Mr. Deyo Apply Properties of Inequality to Solve Multi-Step Inequalities

Title: 4.3 Multi-Step Inequalities Date: Learning Target By the end of the period, I will apply properties of inequality to solve multi-step inequalities. 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 4.3 Pg. 205-206 3) Section ______ TxtBk. Prob. #9-17 Odd,35-39 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 Solve and graph the inequalities. You estimate you can read at least 8 history text pages per day. What are the possible numbers of days it will take you to read at most 118 pages? 6 ≤ 2x – 4

Daily Warm-Up Exercises For use with pages xxx–xxx Solve and graph the inequalities. You estimate you can read at least 8 history text pages per day. What are the possible numbers of days it will take you to read at most 118 pages? 6 ≤ 2x – 4 ANSWER all real numbers greater than or equal to 5 ANSWER at most 15 days

Vocabulary Addition Property of Inequality (P.O.I.) Subtraction P.O.I. Multiplication P.O.I. Division P.O.I. by a Positive(+) Number / by a Negative (-) Number

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

Problem A Solve a multi-step inequality Solve the inequality and graph your solution. -6(x – 5) ≤ 150

The solutions are all real numbers greater than or equal to -20. Problem A Solve a multi-step inequality SOLUTION Solve the inequality and graph your solution. -6(x - 5) ≤ 150 Write original inequality. -6x + 30 ≤ 150 Distributive property -6x ≤ 120 Subtract 30 from each side. x ≥ -20 Divide each side by -6 and Reverse the inequality symbol. ANSWER The solutions are all real numbers greater than or equal to -20.

Problem B Solve a multi-step inequality Solve the inequality and graph your solution. 6x – 7 > 2x + 17

x 6 > 6x – 7 > 2x + 17 6x 24 2x + > 4x 24 > Problem B Solve a multi-step inequality SOLUTION Solve the inequality and graph your solution. 6x – 7 > 2x + 17 Write original inequality. 6x 24 2x + > Add 7 to each side. 4x 24 > Subtract 2x from each side. x 6 > Divide each side by 4. ANSWER The solutions are all real numbers greater than 6.

+c +c −c −c c c −c −c ¿¿ c c −c −c ?? Properties of Inequality (P.O.I.) +c +c −c −c c c −c −c ¿¿ c c −c −c ??

-6y + 5 ≤ -3y - 16 Guided Practice Solve the inequality. Graph your solution. -6y + 5 ≤ -3y - 16

y ≥ 7 -6y + 5 ≤ -3y - 16 -6y ≤ -3y - 21 -3y ≤ - 21 Guided Practice SOLUTION Solve the inequality. Graph your solution. -6y + 5 ≤ -3y - 16 -6y ≤ -3y - 21 -3y ≤ - 21 y ≥ 7 ANSWER

Title: 4.3 Multi-Step Inequalities Date: Learning Target By the end of the period, I will apply properties of inequality to solve multi-step inequalities. 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 4.3 Pg. 205-206 3) Section ______ TxtBk. Prob. #9-17 Odd,35-39 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) When you use the division property of inequality, what happens when you divide by a negative number? When I divide an inequality by a negative number, ___________________________________________ __________________________________________.

Problem A Solve a multi-step problem CAR WASH Gasoline $3.99/gal. rg. unleaded $4.19/gal. supreme Vehicle Wash $5.99 car $6.99 SUV A gas station offers gasoline and car washes at the prices shown. The gas station charges $.10 less per gallon of gasoline if a customer also gets a car wash. What are the possible amounts (in gallons) of regular unleaded gasoline that you can buy if you also get a car wash and can spend at most $30?

($3.99 – 0.10) • G + $5.99 ≤ $30.00 Problem A SOLUTION Solve a multi-step problem SOLUTION Gasoline $3.99/gal. rg. unleaded $4.19/gal. supreme Vehicle Wash $5.99 car $6.99 SUV A gas station offers gasoline and car washes at the prices shown. The gas station charges $.10 less per gallon of gasoline if a customer also gets a car wash. What are the possible amounts (in gallons) of regular unleaded gasoline that you can buy if you also get a car wash and can spend at most $30? STEP 1 Write a verbal model. Then write an inequality. ($3.99 – 0.10) • G + $5.99 ≤ $30.00

G ≤ 6.172236. . . 1 2 3 4 5 6 7 STEP 2 Solve the inequality. Problem A Solve a multi-step problem SOLUTION STEP 2 Solve the inequality. 3.89G + 5.99 ≤ 30.00 Write inequality. 3.89G ≤ 24.01 Subtract 5.99 from each side. G ≤ 6.172236. . . Divide each side by 3.89. You can buy up to slightly more than 6 gallons of gasoline. ANSWER CHECK You can use a table to check the reasonableness of your answer. Gasoline (gal) 1 2 3 4 5 6 7 Total Amount Spent ($) 5.99 9.88 13.77 17.66 21.95 25.84 29.73 33.62

Problem B $3.99/gal. rg. unleaded $4.19/gal. supreme $5.99 car Solve a multi-step problem Gasoline $3.99/gal. rg. unleaded $4.19/gal. supreme Vehicle Wash $5.99 car $6.99 SUV A gas station offers gasoline and car washes at the prices shown. The gas station charges $.10 less per gallon of gasoline if a customer also gets a car wash. What are the possible amounts (in gallons) of supreme gasoline that you can buy if you also get an SUV wash and can spend at most $20?

Problem B Solve a multi-step problem SOLUTION 4.09G + 6.99 ≤ 20.00 Write inequality. 4.09G ≤ 13.01 Subtract 6.99 from each side. G ≤ 3.18909. . . Divide each side by 4.09. You can buy up to slightly more than 3 gallons of gasoline. ANSWER CHECK You can use a table to check the reasonableness of your answer. Gasoline (gal) 1 2 3 4 5 6 7 Total Amount Spent ($) 6.99 11.08 15.17 19.26 27.44 31.53 35.62 39.71

Guided Practice CAMP COSTS You are saving money for a summer camp that costs $1800. You have saved $500 so far, and you have 14 more weeks to save the total amount. What are the possible average amounts of money that you can save per week in order to have a total of at least $1800 saved?

at least $92.86 per week 500 + 14C ≥ 1800 14C ≥ 1300 C ≥ 92.857… Guided Practice CAMP COSTS You are saving money for a summer camp that costs $1800. You have saved $500 so far, and you have 14 more weeks to save the total amount. What are the possible average amounts of money that you can save per week in order to have a total of at least $1800 saved? 500 + 14C ≥ 1800 14C ≥ 1300 C ≥ 92.857… ANSWER at least $92.86 per week

Vocabulary Addition Property of Inequality (P.O.I.) Subtraction P.O.I. Multiplication P.O.I. Division P.O.I. by a Positive(+) Number / by a Negative (-) Number

Title: 4.3 Multi-Step Inequalities Date: Learning Target By the end of the period, I will apply properties of inequality to solve multi-step inequalities. 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 4.3 Pg. 205-206 3) Section ______ TxtBk. Prob. #9-17 Odd,35-39 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

Ticket OUT. You spend $108 on supplies to make picture frames and plan to sell the picture frames for $11 each. What are the possible numbers of picture frames that you can sell in order for your profit to be positive? at least 9 at least 10 Turn to your partner and share your answer. Please use correct answer. Partner B, please share what Partner A told you. at most 10 at most 9

Ticket OUT. You spend $108 on supplies to make picture frames and plan to sell the picture frames for $11 each. What are the possible numbers of picture frames that you can sell in order for your profit to be positive? at least 9 at least 10 ANSWER B Turn to your partner and share your answer. Please use correct answer. Partner B, please share what Partner A told you. at most 10 at most 9