DO MORE! Solve Linear Inequalities(Part 2)

Transcription

1 Directions: Solve and graph the inequality DO MORE! Solve Linear Inequalities(Part 2) b < s 9 2(s 6) Directions: Solve and graph the inequality if possible; if not determine the solutions. 4. 3(x + 4) 3x 5. v + 1 > v 6 Essential Question: How are quantities modeled with equations and inequalities? How are equations and inequalities alike and different? AIM: KWBAT and solve linear in one variable. Standard: MCC9-12.A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Words that describe inequality Greater than at least below fewer than Greater than or equal to at most above Minimum Less than no more than larger than maximum Less than or equal to not equal to smaller than more than > < ( 3 words) ( 1 words)

2 Steps to create inequalities: 1. Read the problem statement first. 2. Reread the scenario and make a list or a table of the known quantities. 3. Read the statement again, identifying the unknown quantity or variable. 4. Create expressions and inequalities from the known quantities and variable(s). 5. Solve the problem. 6. Interpret the solution of the inequality in terms of the context of the problem. Translating phrases into algebraic inequalities. Example 1 A tour bus can seat 55 passengers. Example 2 Camilla is saving to purchase a new pair of bowling shoes that will cost at least $39. She has already saved $19. What is the least amount of money she needs to save for the shoes? Example 3 Juan has no more than $50 to spend at the mall. He wants to buy a pair of jeans and some juice. If the sales tax on the jeans is 4% and the juice with tax costs $2, what is the maximum price of jeans Juan can afford? Example 4 Joe goes to the store with $15 to buy salad. Bags of pre- washed salad are on sale for $2 each. What are the possible numbers of bags Joe can buy? 1. To enter the play area, children must be more than 4 feet tall. 2. As of July 1988, the speed limit on rural interstates in Virginia is 65 mph. 3. An energy- efficient lamp can only be used with light bulbs that are 60 watts or less. 4. Josephine sleeps more than 7 hours each night.

3 5. Jessica makes overtime pay when she works more than 40 hours in a week. So far this week she has worked 29 hours. She will continue to work h hours this week. Write, solve, and graph an inequality to show the values of h that will allow Jessica to earn overtime pay. 6. Penelope s MP3 player has 20 megabytes of memory. She has already downloaded 11 megabytes. She will continue to download m more megabytes. Write and solve an inequality that shows all the values of m that Penelope can download to her MP3 player. 7. Roy works more than 30 hours each week. He has worked 17 hours already. Write and solve an inequality that shows the numbers of hours h that Roy has left to work. 8. Joy wants to save at least $40 for her trip to the amusement park. So far, she has $32. She plans to save d more dollars. 9. Henry s MP3 player has 512MB of memory. He has already downloaded 287MB and will continue to download m more megabytes. Write and solve an inequality that shows how many more megabytes he can download. 10. Eleanor needs to read at least 97 pages of a book for homework. She has read 34 pages already. Write and solve an inequality that shows how many more pages p she must read.

4 11. By selling old CDs, Sarah has a store credit for $153. A new CD costs $18. What are the possible numbers of new CDs Sarah can buy? 12. Phil has a strip of wood trim that is 16 feet long. He needs 5- foot pieces to trim some windows. What are the possible numbers of pieces he can cut? 13. At an online bookstore, Kendra bought 4 copies of the same book for the members of her book club. She got free shipping because her total was at least $50. What was the minimum price of each book? 14. A VHS tape holds at most 360 minutes. A tape already has a 120- minute movie on it. How many 30- minute sitcoms can be recorded on the remaining tape? 15. Alexis is saving to buy a laptop that costs $1,100. So far she has saved $400. She makes $12 an hour babysitting. What s the least number of hours she needs to work in order to reach her goal? 16. Suppose you earn $20 per hour working part time at a tax office. You want to earn at least $1,800 this month, before taxes. How many hours must you work? 17. Hiram earned a score of 83 on his semester algebra test. He needs to have a total of at least 180 points from his semester and final tests to receive an A for his grade. What score must Hiram earn on his final test to ensure his A? 18. Claire purchases DVDs from an online entertainment store. Each DVD that she orders costs $15 and shipping for her order is $10. Claire can spend no more than $100. How many DVDs can Claire purchase?

5 Creating phrases from algebraic inequalities. Example 1 Example 2 Example 3 2x 5 9 2x 6 m + 15 > 6 1. b + 8 > y a 5 < x m + 15 > x t > g > y 5 > 4