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Unit 3 Inequalities Name: ______________________ Period: _____________________ Day Started: _________ Day Completed: _________ Table of Contents Topic Book Pages in Title Essential Questions # Section Packet - What are the inequality 1 Basic Inequalities 3-1 2 symbols and what do they mean? - How do you know when to flip the inequality symbol? How do 3-2 you solve an inequality? 3-3 2 Solving Inequalities - How do you solve an 3-4 3-4 inequality? 3-5 - How do you graph an inequality on a number line? - What key words in a sentence 3-2 imply inequality? Word problems 3-3 3 - How do you write the 5-6 involving inequalities 3-4 inequality that models the word 3-5 problem? -What is a compound inequality? - How do you solve and graph Compound compound inequalities? 4 3-6 7-8 Inequalities - How do you write a compound inequality that models a word problem? 1 Topic 1: Basic Inequalities An inequality is a __________________________ of values. The values are compared using the following signs < > ≤ ≥ Less Than Greater Than Less Than or Equal Greater Than or Equal to to “is less than” “is greater than” “is smaller than” “is larger than” “is at least” “is at most” “is more than” Translate the following sentences to algebraic inequalities 1. Nine more than a number is less than 15. 2. 3 less than a number is less than -6 3. A number increased by 6 is less than or equal to 4. 4. A number decreased by 13 is at most 15. 5. Twice the quantity of a number and 6 is at most 12. 2 Topic 2: Solving Inequalities A _______________________________________ is any/all value(s) that make the inequality _______________. Steps for solving an inequality: 1. Solve like an equality (equation) 2. If you have to divide/multiply by a negative flip the sign. Why do we flip the sign??? Here’s a true statement Divide both sides by -1, do not flip signs Is the resulting a true statement? How do you make it true? ___________ __________ ____________________ ___________ Prove that the same is true for multiplying by a negative. 3 Solve each inequality and graph. 1) g – 5 ≥ 6 2) 1 x ≤3 3) 12 < 3p + 6 2 4) 7 – 2t ≤ 21 5) 4f + 160 ≤ 500 6) -12 > -4x - 8 7) 2 x -5>7 8) 3 < 2d – 5(d + 3) 9) 2m > 4m – 6 3 10) 9y + 3 > 4y - 7 11) 1.5x – 1.2 < 3.1x – 2.8 12) -5(y + 3) – 6 < y + 3 4 Topic 3: Word problems involving inequalities 1) Ms. Chinappi saved $550 to go on a trip 2) Aliyah must sell at least 50 candy bars for a over Columbus Day weekend. The cost of school fund-raiser. She already sold 36 candy the hotel room, including tax is $80 per bars. Write and solve an inequality to determine night. Write an inequality to show the how many more baskets Aliyah must sell for the number of nights I could choose to stay fund-raiser. without going over the amount of money I saved. Know Don’t Know Know Don’t Know 3) Jahmel made a budge and has at most $16 4) Dan earns $5.95 per hour working after to spend on entertainment each week. So far school. He needs at least $215 for his holiday this week, he spent $7.50. Write and solve an shopping. How many hours must he work to reach inequality to determine how much money his goal? Jahmel can spend on entertainment the rest of Know Don’t Know the week. Know Don’t Know 5 5) Jake earns $9.85 per hour working at a 6) Members of the football boosters are planning software company. He wants to earn at least to sell programs at games. The cost to print the $300 a week. How many full hours must he programs is $150 plus $0.50 per program. They work to earn the money? plan to sell each program for $2. How many Know Don’t Know programs must they sell to make a profit of at least $500? Know Don’t Know 7) Tamara has a cell phone plan that charges 8) An online music club has a one-time $0.07 per minute plus a monthly fee of $19.00. registration fee of $13.95 and charges $0.49 to She budgets $29.50 per month for total cell buy each song. If Emma has $50.00 to join the phone expenses without taxes. What is the club and buy songs, what is the maximum number maximum number of minutes Tamara could use of songs she can buy? her phone each month in order to stay within her budget? 6 Topic 4: Compound Inequalities Compound inequality: - Two or more simple inequalities connected by the word ______ or ______. - Also in set theory (last unit), inequalities connected by ______ or ______. Example 1) Write an inequality that represents the set of numbers described and graph the solution. a) All real numbers that are greater than zero and less than or equal to four. b) All real numbers that are at most -3 or more than 0 c) All real numbers that are less than -1 or greater than 2. d) All real numbers that are at least -2 and no more than 3. Example 2) Solving and graphing compound inequalities (including interval notation) a) 18 ≤ 3x ≤ 30 b) 3x + 4 > 10 and x < 5 c) 6x – 5 < 7 or 8x + 1 > 25 d) -6 < -2x + 4 or x > 6 e) -2 ≤ 3x – 8 < 10 f) (3, 5] ∩ [4, 8) g) [-3, 2] (1, 8] h) (-∞, 6] ∩ [2, ∞) i) (3, 6] (-1, 8) Example 3) Write the compound inequality shown by each graph. a) b) 7 On Your Own: Pg. 206: 17-23 odd. 24-27 30-33 Compound Inequalities Applications 1. Write inequalities that describe the elevation of the different regions of Mount Rainer. (a) Timber Region (b) Alpine Region (c) Glacier Region 2. Jonelle just bought a new Toyota Prius. She is estimated to get approximately 51 miles per gallon (MPG) in the city and 48 MPG on the highway. Her tank holds 12 gallons of gas. Write and graph a compound inequality representing how far she can drive with a tank full of gas. 3. Brittany just bought a new Hummer H3. She is estimated to get approximately 14 MPG in the city and 18 MPG on the highway. Brittany has 12 gallons of gas in her tank. Write and graph a compound inequality representing how far she can drive with 12 gallons of gas. 8

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solving inequalities, linear inequalities, inequality sign, linear inequality, Equations and Inequalities, How to, interval notation, number line, absolute value, real numbers

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posted: | 5/1/2010 |

language: | English |

pages: | 9 |

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