Aim #18.1: How do we solve problems with inequalities? What does this mean? You need at least a 65 to pass this class.

Size: px

Start display at page:

Download "Aim #18.1: How do we solve problems with inequalities? What does this mean? You need at least a 65 to pass this class."

Terence Pearson
5 years ago
Views:

1 Copy down tonight's homework HW - Aim 18.1 Aim #18.1: How do we solve problems with inequalities? What does this mean? You need at least a 65 to pass this class. How many passing grades are there? Write this an an inequality? 1

2 1) Explain the meaning of each symbol. a) < b) > c) < d) > 2

3 2) Write a sentence that describes each inequality. a) x < 8 b) -1 > x c) x > -3 d) 9 < x e) x < 3 f) -5 > x 3

4 3) Determine if the following inequalities are true or false. a) 4 < 9 b) -7 > 7 c) 3 > -2 d) 6 < 6 4

5 4) Write an inequality to model each situation. a) An elevator can carry at most 8 people. b) Your SUV can fit a maximum of 7 people. c) You must write a minimum of 3 pages for your English report d) The school track team needs at least 5 runners to compete at Saturdays meet. e) Elephants can drink up to 40 gallons of water at a time. f) Your cousins early morning paper route has more than 32 homes. g) The speed limit is 50 miles per hour. 5

6 4) Write an inequality to model each situation. h) There are more than 25 states in the country. i) A sign on a tunnel says, Maximum height of vehicles is 15 feet. j) Water boils at a temperature of at least 212 o F. k) Your brother had at most 25 people at his party. l) Six times a number increased by 4 is at most fiftyeight. m) Five less than half of a number is at least nine. n) Three times a number increased by six is at least 24. 6

7 4) Write an inequality to model each situation. o) Five more than four times a number is greater than 17. p) Eight less than three times a number is at most 30. q) Sixteen plus three times a number is at least 26. r) The sum of a number and one more than the number is at most 12. s) Four times a number increased by thirteen is less than 16. 7

8 8

9 A) Take out last nights homework HW - Aim 18.1 B) Copy down tonight's homework HW - Aim 18.2 Aim #18.2: How do we solve/graph inequalities? C) Solve and graph: 2x - 5 < 9 9

10 HW Answers 1) Write a sentence that describes each inequality. a) x > -9 b) x < 3 c) 5 > x 2) Determine if the following inequalities are true or false. a) 3 < 3 b) 6 > -6 c) 0 > 4 3) Write an inequality to model each situation. a) A truck can carry at most 5 people. b) You must leave the house at least 15 minutes before the mo c) The maximum speed is 45 miles per hour. d) It takes Mrs. Hadden a minimum of 35 minutes to drive home. 10

11 REMINDER When you multiply or divide by a NEGATIVE, flip the inequality symbol! 11

12 Solve and graph. a) 2d + 5 > 9 b) 3(x 5) < -21 c) d) a 9 < -3 12

13 e) -2n + 5 > -9 f) 4 3x < 19 g) 4(a 5) + 2 > 10 h) a 3(a + 6) >

14 i) 3 - a < 8 j) k) 4x + x 6x > -8 l) 14

15 15

16 Take out last night's homework HW - Aim 18.2 Copy down tonight's homework HW - finish classwork Aim 18.3: How do we review inequalities? Solve and graph. a) -2x - 7 > -1 b) 3(x - 5) < 9 16

17 HW Answers Solve and graph. a) 4(p + 7) < 8 b) -p + 7 > 3 c) d) 4g + g 2g >

18 1) What is the solution of 3 6x < 9? a) x < -1 b) x > -1 c) x < -1 d) x > -1 2) What is the solution of the inequality -8(x + 1) > -32? a) x < 3 b) x > 3 c) x < -3 d) x > -3 3) Define a variable and write an inequality to model each situation. a) A roller coaster can hold at most 22 people. b) Your SUV can fit a maximum of 7 people. c) You must write a minimum of 5 paragraphs for your DBQ. 4) Which value of x is a solution to the inequality -4(x + 1) > 16? a) -2 b) -4 c) -6 d) 0 5) Which inequality is shown on the accompanying graph? a) 1 < x b) 1 > x c) 1 < x d) 1 > x 18

19 6) Which value of x is in the solution set of the inequality -2x + 6 > 22? a) -10 b) -8 c) -6 d) 8 7) Which inequality is shown on the accompanying graph? a) x < 0 b) x > 0 c) x > 0 d) x < 0 8) Solve and graph. a) 3 2x > 27 b) 3(6 x) < 6 c) 13 < 7 3x d) 2x 9 > 1 e) 3(x 2) > -27 f) 5 < 2x

20 9) Which inequality is shown on the accompanying graph? a) x > 3 b) x > 3 c) x < 3 d) x < 3 10) Find all the negative odd integers that satisfy the following inequality. -6x 5 < ) Which value of x is a solution to the inequality -2x + 7 < -5? a) -8 b) -6 c) 6 d) 8 12) Which value of x is a solution to the inequality 5x + 3 > -12? a) -2 b) -3 c) -4 d) -5 13) Which inequality is shown on the accompanying graph? a) x > -3 b) x < -3 c) x < -3 d) x > -3 14) Which value of x is a solution to the inequality 5(x 6) < 15? a) 12 b) 11 c) 10 d) 9 20

21 Copy down tonight's homework HW - Aim 18.4 Test Friday 11/17 - inequalities Aim 18.4: How do we solve inequality word problems? Solve and graph. 3(2x - 4) - 5x < 4x

22 1) Casey goes to an amusement park with her friends. The admission fee to go to the park is $5 and each ride costs $0.60. If Casey has at most $29 to spend, how many rides can she go on? 2) James wants to earn at least $40 this week to go on a ski trip. His dad will pay him $14 to babysit. For washing their cars, his neighbors will pay him $6 per car. If James babysits 2 hours, write and solve an inequality to find out how many cars he needs to wash to earn at least $40. 3) Charles wants to order phone cases over the internet. Each case costs $12.99 and shipping for the entire order is $5.99. Charles has no more than $120 to spend. What is the maximum number of phone cases Charles can order? 22

23 4) The Green Club is raising money for charity. Their goal is to raise at least $250. So far, they have raised $110. If there are 5 days left in the charity drive, how much money on average should they aim to collect each day? Write and solve and inequality. 5) David needs to save $500 to go to Cooperstown for his baseball tournament. He will makes $20 a house for shoveling the snow. If David has already saved $40, what is the minimum number of houses he needs to shovel in order to have enough money? 6) At the county fair, it costs $1.50 to play each game and $2.00 to ride each ride. Kerry has no more than $50 to spend at the fair. If Kerry went on 11 rides, how many games can she play? 23

24 7) The length of a rectangle is 12 and its width is w. The perimeter of the rectangle is, at most, 38. a) Write and solve and inequality that can be used to find the longest possible width. b) What is the longest possible integer value that the width could be? 8) The seventh grade class needs to purchase food for their class picnic which will cost them $215. Each 7 th grader pays $0.85 to attend and each guest pays $1.40. If th graders attend the picnic, what is the minimum number of guests that will need to attend to cover the cost of the food? 9) You want to buy a bike that costs $315. So far you have $116 and you plan to save an additional $25 per week. Write and solve an inequality to find the number of weeks it will take you to save at least $

25 10) The Long Island Railroad changes $3.50 per trip. They also offer a monthly pass for $120. Write and solve and inequality to find how many times a person should use the train so that the pass is less expensive than buying individual tickets. 11) Jason wants to earn at least $30 this week to go to the fair. His dad will pay him $12 to mow the lawn and his neighbors will pay him $8 per car for washing their cars. Write and solve an inequality to find how many cars he needs to wash to earn at least $30. 12) You want to buy the iphone 5 for $200 with the money you make babysitting. If you make $15 per hour, write and solve an inequality to find how many whole hours you must babysit to buy the iphone. 25

26 26

27 Take out last night's homework HW - Aim 18.4 Copy down tonight's homework COMPLETE Classwork Test Friday 11/17 Aim 18.5: How do we solve inequality word problems Day 2? Write as an inequality: You have at most $8 to spend. 27

28 HW Answers 1) Jamie babysits for her neighbor and makes $125 a week. If she has already saved $215, what is the minimum number of weeks she needs to babysit in order to have enough money to buy a $700 ipad? w = number of weeks 125w > 700 w > or more weeks 2) Tanya has a cell phone plan that charges $0.09 per minute plus a monthly fee of $ She budgets $25.80 per month for total cell phone expenses without taxes. What is the maximum number of minutes Tanya could use her phone each month in order to stay within her budget? m = number of minutes 0.09m + 15 < m < minutes or less 3) Mrs. Aloia has $60.00 to spend on bagels and muffins for a breakfast. Bagels cost $1.50 each and muffins cost $2 each. If Mrs. Aloia bought 10 bagels, what is the maximum number of muffins that Mrs. Aloia can buy? m = number of muffins 2m (10) < 60 m < bagels or less 28

29 1) When 3x + 2 < 5(x 4) is solved for x, the solution is (1) x < 3 (2) x > 3 (3) x < -11 (4) x > 11 2) Given 2x + ax 7 > -12, determine the largest integer value of a when x = -1. 3) Solve the inequality below to determine and state the smallest possible value for x in the solution set: 3(x + 3) < 5x 3 4) An online book club has a one-time registration fee of $12 and charges $3 to buy each book. How many books can Jennifer purchase if she has at most $50 to join the club and buy books? 29

30 5) What is the solution to 2h + 8 > 3h 6? (1) h < 14 (2) h < 14 5 (3) h > 14 (4) h > ) Pat currently has $300 saved up. At the end of each week, Pat gets $75 for his allowance. How many weeks will it take for Pat to have at least $700? 7) The cost of a pack of chewing gum in a vending machine is $0.75. The cost of a bottle of juice in the same machine is $1.25. Julia has $22.00 to spend on chewing gum and bottles of juice for her team and she must buy seven packs of chewing gum. If b represents the number of bottles of juice, which inequality represents the maximum number of bottles she can buy? (1) 0.75b (7) > 22 (2) 0.75b (7) < 22 (3) 0.75(7) b > 22 (4) 0.75(7) b < 22 8) Connor wants to attend the town carnival. The price of admission to the carnival is $4.50, and each ride costs an additional 79 cents. If he can spend at most $16.00 at the carnival, which inequality can be used to solve for r, the number of rides Connor can go on, and what is the maximum numbers of rides he can go on? (1) r < 16.00; 3 rides (2) r < 16.00; 4 rides (3) r < 16.00; 14 rides (4) r < 16.00; 15 rides 30

31 9) Solve for x algebraically: 7x 3(4x 8) < 6x x a) If x is a number in the interval 4 < x < 8, state all the integers that satisfy the given inequality. 10) Solve and graph: 4(x - 7) > 6x x 11) At the movies a bag of popcorn costs $3.50 and a bottle of mineral water costs $2.75. If Caitlyn has $18 and bought 2 bottles of water, what is the maximum number of bags of popcorn can she buy? 12) Determine the smallest integer that makes -3x + 7 5x < 15 true. 31

Algebra 1 Keystone Remediation Packet Module 1 Anchor 3

Algebra 1 Keystone Remediation Packet Module 1 Anchor 3 A.1.1.3.1 Write, solve, and/or graph linear inequalities using various methods. A.1.1.3.1.1 Write or solve compound inequalities and/or graph their