XEI 506 Lessons/Notes CRS SKILL Expressions Equations and Inequalities XEI 506 Name_________________________________________ Period____________ LEVEL Level 1 – ALL students must attain mastery at this level Level 2 – MOST students will attain mastery of the focus skill in isolation . Level 3 – SOME students will attain mastery of focus skill with other skills Level 4 – SOME students will attain mastery of focus topics covered in a more abstract way Level 5 – FEW students will attain mastery of the extension skill. DESCRIPTION NCP 404 Exhibit knowledge of number concepts including inequalities XEI 506 Solve first degree inequalities that do not require reversing the inequality sign XEI 603 Solve linear inequalities that require reversing the inequality sign XEI 604 Solve absolute value equations VOCABULARY Absolute Value REQUIRED SKILLS TO MASTER http://www.mrmaisonet.com/index.php?/Inequality-­‐Quiz/Quiz-­‐Practicing-­‐Inequalities.html Select (Quiz –Practicing Inequalities) Additional KHAN Skills One –step inequalities Using inequalities to describe real-­‐world contexts Multi-­‐step linear inequalities Level 1 a. Represent each of the following as an algebraic inequality. a. 57 is greater than x. b. x is less than or equal to -­‐24. c. 6 is greater than x. d. -­‐99 is less than x. 1 e. x is less than or equal to -­‐15. f. -­‐38 is greater than x. g. x is greater than 98. h. x is at most 30 i.
the sum of 5x and 2x is at least 14 j.
the product of x and y is less than or equal to 4 k. 5 less than a number y is under 20 2. Which statement is modeled by 2p + 5 < 11? a. The sum of 5 and 2 times p is at least 11. b. Five added to the product of 2 and p is less than 11. c. Two times p plus 5 is at most 11. d. The product of 2 and p added to 5 is 11. 3. An electronics store sells DVD players and cordless telephones. The store makes a $75 profit on the sale of each DVD player (d) and a $30 profit on the sale of each cordless telephone (c). The store wants to make a profit of at least $255.00 from its sales of DVD players and cordless phones. Which inequality describes this situation? a. 75d + 30c < 255 b. 75d + 30c > 255 c. 75d + 30c ≤ 255 d. 75d + 30c ≥ 255 4. Mrs. Smith wrote "Eight less than three times a number is greater than fifteen" on the board. If x represents the number, which inequality is a correct translation of this statement? a.
b.
c.
d.
2 4 5
2
5. Which of the following lists the fractions , , and in order from least to greatest? 7 9
3
a.
2 4 5
< < 3 7 9
d.
5 2 4
< < 9 3 7
b.
4 5 2
< < 7 9 3
e.
5 4 2
< <
9 7 3
c.
4 2 5
< < 7 3 9
Level 2 Inequality graphing on the number line > Greater than open circle Shade right ≥ Greater than or closed circle equal to < Less than open circle Shade left ≤ Less than or closed circle equal to Solve each inequality. Then check your solution, and graph it on a number line. 6. a -­‐ 12 < 6 7. 2x ≤ x + 1 1
8. x + 3 > 4 9. 2x + 3 > x + 5 3 1 1
10. x + 8 < 2 11. 3x – 9 ≤ 2x + 6 12. 2.17x -­‐ 0.23 < 0.75 -­‐ 1.17x 13. 3(r -­‐ 2) > 2r + 4 Level 3 14. If 5 times a number is increased by 4, the result is at least 19. Find the least possible number that satisfies these conditions. 15. The sum of twice a number and 5 is at most 15. What are the possible values for the number? 4 16. The cost of a gallon of orange juice is $3.50. What is the maximum number of containers you can buy for $15? 17. Three times a number increased by 8 is no more than the number decreased by 4. Find the possible values of the number. 18. Two-­‐thirds of a number plus 5 is greater than 12. Find the possible values of the number. 19. Four times a number is greater than − 48 . What are the possible values for the number?
20. The quotient of a number and 15 is no greater than 450. What are the possible values for the number? 21. Adrian works in New York City and makes $42 per hour. She works in an office and must get her suit dry cleaned everyday for $25. If she wants to make more than $260 a day, at least how many hours must she work? 5 22. Your brother has $2,000 saved for a vacation. His airplane ticket is $637. Write and solve an inequality to find out how much he can spend for everything else. 23. A club can buy ready-­‐made shirts for $14.50 each. Alternately, it can buy plain T-­‐shirts for $6.25 each, fabric paint for $35.70, and a pack of stencils for $8.50. For how many shirts is stenciling plain T-­‐shirts cheaper than buying ready-­‐made shirts? 24. Members of the band boosters are planning to sell programs at football games. The cost to print the programs is $150 plus $0.50 per program. They plan to sell each program for $2. How many programs must they sell to make a profit of at least $500? 25. The cost per month of making n number of wooden toys is C = 3n + 30 . The income from selling n toys is I = 6n . How many toys must the company make to get a profit (I > C) ? 26. Al earns $5.95 per hour working after school. He needs at least $215 for his holiday shopping. How many hours must he work to reach his goal? 6 Level 4 27. Caitlyn is shopping online to find a new television for the community center where she volunteers. She wants a
television with at least a 26 inches screen.
a. Write an inequality to show how much money, m, the center will need to spend.
Television Prices
Screen Size
Price
22 inch
$300
26 inch
$330
32 inch
$370
40 inch
$420
b. Caitlyn drew the graph to the right to represent the solution
to her inequality. Why do you think she drew a solid circle at
330?
c. The center has a stand for the television that will support up to 30 lbs. of weight. Draw a graph to show how much
the television she buys can weigh.
28. Solve the inequality: 3x – 15 > 12 How is solving the inequality above similar to solving the equation 3x – 15 = 12? 29. Caitlyn plans to use money from the community center’s savings account to buy a video game system. She also needs to leave at least $129 in the savings account to buy some softball equipment. a. The inequality a – 129 > 250 represents the situation where a represents the amount of money the center has in its savings account. What does the expression a – 129 represent? 7 b. Solve the inequality. c. What does the solution mean? d. Use the number line below to show all possible values for a. 30. The center rents rooms for an hourly rate, plus a set-­‐up fee. Room Rentals Room Rental Rate per hour Set Up Fee Main Hall $15 $40 Dining Room $12 $80 A group has $140 to spend. The inequality 15h +40 < 140 represents the cost to rent the main hall, where h represents the number of hours the group can rent the room. a. Solve the inequality. 15h +40 < 140 b. The same group is also considering renting the dining room. Write and solve an inequality to represent this situation. c. Which room should the group rent? Why?
8 31. Tony’s parents are choosing a new long distance phone plan. The phone company offers two plans. With plan 1, a
long distance call costs 43 cents plus 2 cents per minute. With plan 2, a long distance call costs 25 cents, plus 4
cents per minute. Tony’s mom makes a lot of long class, so she wants to know which company is a better deal for
longer phone calls.
a. Write an expression to represent plan 1: _________________________________________
b. Write an expression to represent plan 2: _________________________________________
c. Write an inequality that represents when plan 1 is less than plan 2.__________________________
d. Solve the inequality above.
e. What advice would you give Tony’s mom based on your solution? Which plan should she go with? Why? 32. You get a new x box for your birthday from your parents and $175 from your grandparents. You want to use the $175 to buy some video games for your x box. Games are on sale for $35 each at Target. a. The inequality 175 – 35g > 0 represents the number of games that you can buy. Why is the inequality > 0? 9 b. Solve the inequality below. c. What does your solution mean? d. Graph the solution on a number line. e. Could you have g be a negative number in this situation? For example can g = -­‐ 4? Why or why not? Level 5 Investigation In this investigation you will analyze the properties of inequalities and discover some interesting results. First we will act out operations on a number line in the front of the room. 1. Choose two walkers, one announcer and one recorder. Walker A stands in front of the room at position 2. Walker B stands in front of the room at position 4.The announcer asks the class what symbol should be put between the two numbers > or <. The recorder records the symbol. 2. The announcer tells the walkers what operation to use on their number. The walkers move to the appropriate location. The recorder records the new locations. The announcer asks the class what symbol should be put between the two numbers > or <. The recorder records the symbol. 3. Repeat step 2 for each operation in the table below. Operation Walker A’s Position Inequality Symbol > or < Walker B’s Position Starting # Add 2 Subtract 3 Add -­‐2 Subtract -­‐4 Multiply by 2 Subtract 7 Multiply by -­‐3 Add 5 Divide by -­‐4 Subtract 2 Multiply by -­‐1 2 4 If you ___________ or ____________by a negative
number, the inequality symbol__________.
10 33. −7x + 20 > −22 34. −3p + 7 ≤ −23 35. −50 ≥ −5x +15 36. −510 < −5(x + 2) 11 Absolute Value 37. Solve each inequality. Be sure to check your answers. a.
n + 9 = 1 c. 8 − 6n = 32 e. x − 2 = −3 b. − 7 x = 28 d. −9 + p + 5 = 24 f. 2 x − 2 = 6
38. Determine which of the following are always true. Write TRUE of FALSE. For those that are FALSE provide a counter-­‐example (a specific example that prove the statement false 12