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Solving and Graphing Linear Inequalities Chapter Questions

1. How do we translate a statement into an inequality?

2. Explain the steps to graphing an inequality on a number line.

3. How is solving an inequality much like solving a linear equation?

4. What does the “and” & “or” tell us in a compound inequality?

5. When do the special cases happen with compound inequalities?

6. How do graphs of linear inequalities compare with graphs of equations?

7. How do you determine what type of line to use?

8. How do you determine where to shade?

9. How is a system of inequalities graphed?

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Solving Linear Inequalities Chapter Problems

Simple Inequalities Involving Addition and SubtractionClasswork

1. Solve, check and graph the following inequalities.a. x+5>10b. x+3<−2c. 7≥ x+11d. x – 3≤−5e. x – 7>3f. −2+x≥−2g. −9≤ x –3h. x+0.5<4i. −3.75≤x –1.25j. 8.7> x+2.2

2. Write an inequality for each sentence below and then solve and check it.a. The sum of w and nine is less than 18.b. g decreased by 25 is at most five.c. The difference of a number and six is no less than 15.d. 14 is more than the sum of ten and a number.e. 25 plus a number is at least 13.

3. Suppose you must maintain at least $500 in your checking account in order to have free checking. Your balance is $542 and then you write a check for $57. How much do you need to deposit in order to keep your free checking? Write an inequality and solve.

4. You need no more than 2,200 calories in a day. You had 650 calories at breakfast and 825 calories at lunch. At most, how many calories, c can you eat for dinner? Write an inequality and solve.

Homework

5. Solve, check and graph the following inequalities.a. x+7>−2b. x+3≤−3c. −8<x+15d. x – 4≤1e. x – 1>6f. −7+x ≥−11g. −6≤ x – 2h. x+2.5<6i. −5.5≤x –3.25j. 7.9>x+4.4

6. Write an inequality for each sentence below and then solve and check it.a. The difference of a number and seven is at most 16.b. 18 is less than a number plus 7c. h decreased by 3 is more than 1.d. 14 is greater than or equal to the sum of 18 and a number.e. The sum of b and 22 is at least 6


7. Suppose you must maintain at least $500 in your checking account in order to have free checking. Your balance is $612 and then you make a deposit of $79. How much can you withdraw and still keep your free checking? Write an inequality and solve.

8. You need no more than 2,200 calories in a day. You had 720 calories at breakfast and plan on having 1,000 calories at dinner. How many calories, c can you eat for lunch? Write an inequality and solve.

Simple Inequalities Involving Multiplication and DivisionClasswork

9. Solve, check and graph the following inequalities.a. 5 x>−25b. −7 x≤−21c. 18>2 xd. 25 x≥100e. −30≤−6 xf. 10 x<0g. 8 x≥24h. 40≤−8 xi. 20 x≥30j. 350>−70 x

10. Solve, check and graph the following inequalities.

a.x5≥2

b.x2<14

c. −3≤ x−6

d.x

−9>1

e.x

−4≥−3

f.x3≤3

g. 0≤ x8

h. −1≥ x2.5

i.x

−1<2.2


j.x

−1.5>−10

11. Write an inequality for each sentence below and then solve and check it.a. The product of r and 5 is no more than 55.b. The quotient of v divided by -4 is greater than or equal to 2.c. Half of d is greater than 40.d. Twice a number is at most 24.e. One-fourth of y is less than or equal to -12.f. The product of -8 and x is no less than -64.

12. What happens to the inequality symbol when you do each of the following to both sides of an inequality?

a. Multiply by a positive numberb. Divide by a positive numberc. Add a negative numberd. Subtract a negative numbere. Divide by a negative numberf. Multiply by a negative number

Homework

13. Solve, check and graph the following inequalities.a. 4 x≤−16b. 32≤8 xc. −7 x>49d. −5 x<−55e. 13 x≥0f. 60<12 xg. 66>−3xh. −6 x≥360i. −2 x≥17j. 26<4 x

14. Solve, check and graph the following inequalities.

a. 5≤ x3

b.x3←3

c.x

−8≥0

d.x3>11

e. 4 ≤ x−1


f. −4≥ x−6

g.x

−4≥−1.5

h.x4≤12

i.x

−6>−9

j.x

−2<3.3

15. Write an inequality for each sentence below and then solve and check it.a. Four times a number n is no more than 24.b. One-third of m is greater than 9.c. The product of -9 and g is at most 81.d. Half of d is less than or equal to 16.e. The quotient of v divided by -6 is less than 4.f. The product of 7 and x is no less than -42.

Two-Step and Multi-Step Inequalities Classwork

16. Solve, check and graph the following inequalities.a. 10+7 x<17

b. −1+3 x≥−28

c. −4 x+2>−46

d. 3+5 x+3 x≤19

e. −6 x – 6+3 x>−24

f. −4 –2 x+5 x ≤8

g. 6 x – 8>1+3 x

h. 3 x – 9>−41+7x

i. 4 (−7+3 x )≥32

j. 5(−7 x+8)≤275

k.34x−1

2≤−1

4


l. −x+67< 3

28

17. Write an inequality for each situation, then solve.a. You want to spend $20 for a taxi ride. Before you go anywhere, the taxi driver sets the meter

the initial charge of $2. The meter adds $1.50 for each mile and you plan on giving a $2 tip, what is the farthest you can go?

b. On a trip from New Jersey to Florida, your family wants to travel at least 436 miles in one day from 8am to 5 pm. You plan on only stopping for a total of 1 hour. What must your average speed be?

c. The maximum weight in an elevator is 1500 pounds. There are 7 people in the elevator with an average weight of 185 pounds. What is the maximum the weight for the 8th person that will keep the total weight within the safety codes?

d. A male gymnast is participating a 6-event competition. Each event is scored on a ten-point scale. He scored an 8.7 in the floor exercise, an 8.5 in the vault, a 9.2 on the pommel horse, a 9.0 on the horizontal bar, and a 9.5 on the still rings. What is the remaining score required in his last event, the parallel bars, for his average score to be at least a 9.1?

Homework

18. Solve, check and graph the following inequalities.a. 5 x+1>51

b. 6 x+6≤24

c. −6 x – 3>−63

d. 4 –3 x – 5x ≥36

e. 3+x+6 x<−53

f. 2+2 x≤3x+2

g. −8+7 x ≤4 x−52

h. 2 x+8>−x−1

i. 4 (−3 x−5)<−164

j. 6(3x+9)≥126

k.23x+ 4

7> 31

42


l.−14

−23x≤ 5

44

19. Write an inequality for each situation, then solve.a. You have $50 to spend at the boardwalk. Tickets for the rides cost $1.50 and parking is $9.

What is the most number of tickets you can buy?

b. You are shopping at the mall and have less than $75 to spend. If you bought 3 shirts and spent $18 on snacks, how much could one shirt be, is all were the same price?

c. The maximum weight in an elevator is 1500 pounds. There are 8 people in the elevator with an average weight of 165 pounds. What is the maximum the weight for the 9th person that will keep the total weight within the safety codes?

d. A male gymnast is participating a 6-event competition. Each event is scored on a ten-point scale. He scored an 8.9 in the floor exercise, an 8.7 in the vault, a 9.4 on the pommel horse, and a 9.7 on the still rings. He has two events remaining, the parallel bars and the horizontal bar. What must his average score be in these two events for his average score to be at least a 9.3?

Compound Inequalities & Special CasesClasswork

20. Write the compound inequality for the graph below.





24. Solve each inequality and graph the solution on a number line.a. 7≤ x+4≤10b. 4 ≤x+6≤−2c. 15≤x –3≤9d. 3 x>−9∧8≤2 xe. x+3>5∧−4 x ≥−8f. 3 x≤5∧2 x – 2≤−3g. −3 x>−12∧2 x≥6h. x+3>15∨x –7≤−3i. 4 x≥−12∨2x>12j. 2 x+4≥12∨3 x+12≤15k. 5 x+7<12∨−7 x ≥−21l. 4 x≤20∨3 x+1>−5

25. Model each situation with an inequality and solve.a. Your friend is on a diet. He is supposed to eat at least 1500 but no more than 1800 calories

per day. Before dinner he has had 1050 calories. What number of calories should he eat at dinner?

b. To get an A in class your total points must be between 690 and 750, inclusive. If you have 652 points before the last test. What possible numbers of points could you earn and still get an A in the class.

c. Five decreased by half of a number is less than 7 or greater than 10. Write an inequality to represent the possible values of the number.

Homework






30. Solve each inequality and graph the solution on a number line.a. −4<x+2<9b. 7≤3– 2x<11c. 4 ≤x+3≤9d. x≥0∧x<25e. 8 x≥−64∧8>4 xf. −2>3 x+7∧3 x+1≤−14g. x+3<12∧4 x≥24h. −9 x – 3<6∨3 x+5≥26i. 6 x – 8≥10∨−9 x>−9j. 10 x≤−20∨20 x≥40k. −4 x+3≥−17∨4 x – 8≥4l. −7 x+10≤31∨10 x+20≤−50

31. Model each situation with an inequality and solve.a. The sum of any two sides of a triangle is greater than the length of the third side. If two sides

of a triangle are 5 inches and 17 inches. Find the range of values for the lengths of the third side.

b. A gymnast wants her average score after 3 events to be between 9.0 and 10. If she scores an 8.7 and 9.1, what possible values for the third event will make her average between 9.0 and 10?

c. Three more than quadruple a number is at least 31 or less than -3. Write a compound inequality that represents the possible values of the number.

Graphing Linear Inequalities Classwork

PARCC-type questionsGraph each linear inequality.32. 2 y – 4 x ≤−233. y<10 x+434. y ≥8 x35. y>−½ x – 436. −3 y<−9 x+337. 6 x – 4 y<−1238. 16 x+6 y>36

39. y ≥ 65x−8y


40. Suppose your class is raising money for their school trip. You make $5 on each smoothie and $3 on each soft pretzel that you sell. Let x represent the number of smoothies sold and y represent the number of soft pretzels sold. How many items of each type must you sell to raise more than $150?Part AWrite a linear inequality that describes the situation.

Part BGraph the linear inequality.

Part CWrite two possible solutions to the problem.

41. Student Council is selling tickets to the Fall Ball Dance. Tickets cost $6.00 per person, or $10 per couple. To cover the expenses required, they need to make at least $1,450. Let x represent the number of individual tickets sold, and y represent the number of couple tickets sold.Part AWrite a linear inequality to model the situation.


Part CWhich of the following are solutions to the inequality? Select all that apply.

a. (0, 145)b. (80, 80)c. (120, 100)d. (200, 20)e. (240, 10)

42. Audra is buying almonds and cashews for a party. She can spend no more than $45. Almonds cost $6.50 per pound and cashews cost $7 per pound. Let x represent the number of pounds of almonds and y represent the number of pounds of cashews.Part AWrite a linear inequality to model the situation.

Part BGraph the linear inequality


a. (1, 6)b. (2, 4)c. (3, 4)d. (4, 3)e. (5, 1)

Homework

PARCC-type questionsGraph each linear inequality.43. y ≥−444. x+4 y<845. −5 x+4 y ≥−24


46. y ≤ 35x+5

47. 2 x+3 y<−1548. y>−2 x+7

49. y ≤ 49x−6

50. – x+3 y<–12

51. Suppose that you exercise by either running 5 miles per day or rollerblading 10 miles per day. Your goal is to cover a distance of at least 150 miles. Let x represent the number of days running and y represent the number of days rollerblading.Part AWrite a linear inequality that describes the situation.


Part CWrite two possible solutions to the problem.

52. The senior class is selling pizza kits to fund their senior trip. Single slice pizza kits sell for $9.50, and full pizza pie kits sell for $15.00. To lower the cost of their senior trip, each student needs to make at least $600. Let x represent the number of single slice pizza kits sold, and y represent the number of full pizza pie kits sold.Part AWrite a linear inequality to model the situation.



a. (10, 35)b. (15, 30)c. (25, 20)d. (35, 20)e. (60, 0)

53. Jack is filling a bathtub to give his child a bath. The cold water flows at a rate of 3.5 gallons of water per minute. The hot water flows at a rate of 2.5 gallons per minute. Jack wants less than 45 gallons of water in the tub. Let x represent the time that the cold water is turned on and y represent the time that the hot water is turned on.Part AWrite a linear inequality to model the situation.

Part BGraph the linear inequality


a. (2, 16)b. (4, 12)c. (5, 10)


d. (8, 6)e. (12, 2)

Solving Systems of Inequalities by Graphing

ClassworkPARCC-type QuestionsGraph the solution set of each system of linear inequalities in a coordinate plane.

54. y ≤ 52x−2

y ≥ 12x+2

55. y ≤ 14x−1

y<5 x−5

56. y>−13x−3

y ≤ 53x+3

57. y>2 x –53 x+4 y<12

58. x+ y≥−35 x− y ≤−3

59. Mrs. Petal is designing a rectangular flower garden with a fence around it. She can use no more than 100 feet of fencing. She wants the length to be at least 24 feet and the width to be at least 12 feet. Let x represent the length and y represent the width of the garden. Part AGraph the solution set of the system of linear inequalities in a coordinate plane.

Part BWhich of the following are solutions to the system of inequalities? Select all that apply.

a. (28, 16)b. (30, 22)c. (36, 18)d. (38, 12)e. (26, 26)

Part CGiven the conditions in Part A, if Mrs. Petal determines that the length is 30 feet, what is the maximum number of feet that the width can be?

Part DGiven the conditions in Part A, if the length is twice the width, what is the maximum number of feet that the width can be? Round your answer to the nearest whole number.


60. Student Council is selling tickets to the Fall Ball Dance. Tickets cost $6 per person, or $10 per couple. To cover the expenses required, they need to make at least $1,850. However, no more than 350 people can fit in the gym. Let x represent the number of individual tickets sold, and y represent the number of couple tickets sold. Part AGraph the solution set of the system of linear inequalities in a coordinate plane.


a. (50, 150)b. (175, 100)c. (200, 75)d. (300, 50)e. (275, 25)

Part CGiven the conditions in Part A, if Student Council sold 200 individual tickets, then how many couple tickets need to be sold for Student Council to meet their goal?

Part DGiven the conditions in Part A, if Student Council prefers to sell individual tickets over couple tickets, what is the maximum number of individual tickets that can be sold that would allow them to meet their goal? Round your answer to the nearest whole number.

HomeworkPARCC-type QuestionsGraph the solution set of each system of linear inequalities in a coordinate plane.

61. y< 12x+2

y ≥3 x – 3

62. y ≥−x+5 y ≤3 x−4

63. y< 14x

y ≤−x+4

64. y>2 x+42 x− y≤ 4

65. 3 x− y ≥−1 x+ y≤−3

66. The owner of Pam’s Produce Market orders mangoes and avocados. She wants to buy at least 120 pounds of produce, but cannot spend more than $200. Mangoes are $1.70 per pound and avocados are $1.30 per pound. Let x represent the pounds of mangoes and y represent the pounds of avocados.Part AGraph the solution set of the system of linear inequalities in a coordinate plane.



a. (20, 60)b. (30, 90)c. (55, 40)d. (60, 70)e. (65, 80)

Part CGiven the conditions in Part A, if the owner determines that 70 pounds mangos will be purchased, what is the minimum amount of avocados that can be purchased?

Part DGiven the conditions in Part A, if the owner prefers selling mangos to avocados, what is the maximum amount of mangos that can be purchased? Round your answer to the nearest whole number.

67. You can work a total of no more than 42 hours each week at your two jobs. Babysitting pays $8 per hour and when you work as a tutor, you earn $15 per hour. You need to earn at least $420 per week. Let x represent the number of hours babysitting, and y represent the number of hours that you tutor. Part AGraph the solution set of the system of linear inequalities in a coordinate plane.


a. (20, 20)b. (30, 15)c. (40, 5)d. (10, 35)e. (15, 25)

Part CGiven the conditions in Part A, if you work for 14 hours tutoring, what is the minimum number of hours you would have to babysit to earn at least $420? Give your answer to the nearest hour.

Part DGiven the conditions in Part A, if you prefer babysitting to tutoring, what is the maximum number of hours that you can babysit and still earn at least $420? Round your answer to the nearest whole number.


Solving and Graphing Linear Inequalities Unit Review1. Which value(s) of x is in the solution set of the inequality 7(x + 1) > -14? Select all that apply.

a. -22b. -2c. -1d. 1

2. Which graph represents the solution set for: 1/5 + 1/3 x ≤ 4/15

a.

b.

c.

d.

3. Which type of line is used when graphing -4x - 3y ≤ 10a. Dashedb. Solidc. No line

4. Determine which points are solutions to each linear inequality 4x - 2y ≤ 6. Select all that apply.a. (-7, 9) b. (0, -4) c. (-1, -8)d. (-10, -100)e. (-2, 1)f. (3, 2)

5. Determine which points are solutions to the system of linear inequalities. Select all that apply.−5 x−3 y>103 x+ y<4

a. (-2, 0)b. (0, -2)c. (-3, -1) d. (1, -4)e. (-4, 3)f. (1, -2)

6. Which linear inequality describes the graph to the right?a. 4y < -3x +12

b. 3x – 4y > 12

c. y > ¾ x + 3

d. 3x + 4y > 12


7. Which linear inequality describes the graph to the right?a. y ≥ -10x + 11

b. 10x + 2y ≤ 11

c. y ≥ -5x + 5.5

d. 10x – 2y ≤ 11

8. Which graph represents the following system of inequalities?-x + y < - 12x + y ≥ 2

a. b. c.

9. Which of these points is a solution of the system y >- 2x + 3 and -x + y > 0?a. (2, -6)b. (-1, -2)c. (5, 2)d. (1, 3)

10. Which coordinate point is in the solution set for the system of inequalities shown in the accompanying graph?

a. (1, 3)b. (-1, 3)c. (1, –4)d. (-3, 0)

11. Solve and graph: 3x + 2 < 0


12. Solve and Graph: ¼ x – 3/5 ≥ 2/3

13. Solve and Graph: 5x – 4 ≥ 6 and 7x + 11 < 32

14. Solve and Graph: 22 ≥ 2(2m – 1) or 5 – 3m ≤ -13

15. Solve and Graph: 7x + 4 < 18

16. Graph: 3x + y > 1 17. Graph: y← 19x−1

18. Write a linear inequality with (0, 4) as a solution.

19. Write a linear inequality with (4, -2) on the boundary but not a solution.

20. Write the inequality for the graph below.




23. Most snakes live where the temperatures ranges from at least 75°F to no more than 90°F. Graph the temperatures where snakes will not thrive.

24. Write the system of inequalities graphed below

25. Maria is in charge of organizing the school’s holiday carnival. She is setting up booths in the gym. Each booth can have three players. Maria plans on setting up at least 22 booths in the gymnasium. Part AWrite an inequality to model this situation.

Part BWhat is the minimum number of players that can compete in the booths at the holiday carnival?


26. The fast food restaurant in town is selling hot dogs and hamburgers to raise money for a local charity. They are selling the hot dogs for $2.00 each and the hamburgers for $3.50 each. Their goal is to raise at least $1,000 for the charity and cook no more than 400 hot dogs and hamburgers. Part ALet x represent the number of hot dogs sold and let y represent the number of hamburgers sold. Write a system of inequalities that describes the situation.

Part BGraph the inequalities.

Part CWrite three possible solutions to the problem.

Part DIs “200 hot dogs and 200 hamburgers” a solution? Justify your answer.


Answer Key1.

a. x>5

b. x<-5

c. -4≥x

d. x<-2

e. x>10

f. x≥0

g. -6<x

h. x<3.5

i. -2.5<x

j. 6.5>x

2. a. w+9<18 w<9b. g-25<5 g<30c. x-6≥15 x≥21d. 14≥10+x 4≥xe. 25+x≥13 x≥-12

3. 542-57+x≥500 x≥15

4. 650+825+c<2200 c<725

5. a. x>-9

b. x<-6

c. -23<x

d. x<5

e. x>7

f. x≥-4

g. -4<x

h. x<3.5

i. -2.25<x

j. 3.5>x

6. a. x-7<16 x<23b. 18<x+7 11<xc. h-3>1 h>4d. 14≥18+x -4≥xe. b+22≥6 b≥-16

7. 612+79-x≥500 191≥x

8. 720+1000+c<2200 c<580

9. a. x>-5

b. x≥3

c. 9>x

d. x≥4

e. 5≥x

f. x<0

g. x≥3

h. 5≥x


i. x≥3/2

j. 5<x

10. a. x≥10

b. x<28

c. 18≥x

d. x<-9

e. x<12

f. x<9

g. 0<x

h. -2.5≥x

i. x>-2.2

j. x<15

11. a. 5r<55 r<11b. v/(-4) ≥2 v<-8c. (d/2)>40 d>80d. 2x<24 x<12e. (y/4) <-12 y <48f. -8x≥-64 x<8

12. a. Stays the sameb. Stays the samec. Stays the samed. Stays the samee. Change to the opposite inequality sign f. Change to the opposite inequality sign

13.

a. x<-4

b. 4<x

c. x<-7

d. x>11

e. x≥0

f. 5<x

g. -22<x

h. x<-60

i. x<-8.5

j. 6.5<x

14. a. 15<x

b. x<-9

c. x<0

d. x>33

e. -4≥x

f. 24<x

g. x<6

h. x<48

i. x<54


j. x>-6.6

15. a. 4n<24

n<6b. (m/3)>9

m>27c. -9g<81

g≥-9d. (d/2) <16

d<32e. (v/-6)<4

v>-24f. 7x≥-42

x≥-6

16. a. x<1

b. x≥-9

c. x<12

d. x<2

e. x<8

f. x<4

g. x>3

h. 8>x

i. x≥5

j. x≥-47/7

k. x<1/3

l. x>.75

17. a. 2+1.5x+2<20

x<32/3b. 9x-1x≥436

x≥54.5c. 7 (185 )+x≤1500

x≤205 pounds

d.8.7+8.5+9.2+9.0+9.5+x

6≥9.1

x≥9.7

18. a. x>10

b. x<3

c. x<10

d. x<4

e. x<-8

f. 0<x

g. x<-44/3

h. x>-3

i. x>12

j. x≥4

k. x>.25

l. x≥-6/11

19. a. 1.50 x+9≤50

27


b. 3 x+18<75x<19

c. 8 (165 )+x≤1500x≤180 pounds

d.8.9+8.7+9.4+9.7+2x

6≥9.3

x≥9.55

20. -5<x<521. -7<x<322. x<-4 and 0<x23. x<1 and x>324.

a. 3<x<6

b. x≥-2 and x<-8

c. x<12 and x≥18

d. x>-3 and 4<x

e. x>2 and x<2

f. x< (5/3) and x<-.5

g. x<4 and x≥3

h. x>12 or x<4

i. x≥-3 or x>6

j. x≥4 or x<1

k. x<1 or x≥3

l. x<5 or x>2

25. a. 450<x<750

b. 38<x<398c. x < -10 or x > -4

26. -4<x<6

27. -9<x<-3

28. x<-2 and 5<x

29. x<-6 and -2<x

30. a. -6<x<7

b. -2≥x>-4

c. 1<x<6

d. x≥0 and x<25

e. x≥8 and 2>x

f. -3>x and x< -5

g. x<9 and x≥6

h. x>-1 or x≥ 7

i. x≥ -3 or x<1

j. x< -2 or x≥ 2

k. x< 6 or x≥3

l. x≥-3 or x< -7

31. a. 12<x<22 b. 9.2 < x< 12.2 c. x←1.5∨x≥7


CLASSWORK32.

33.

34.


2y – 4x ≤ -2 +4x +4x2y ≤ 4x – 2y ≤ 2x – 1 (Solid boundary line)

test (0,0)

0 ≤ 2(0) – 10 ≤ -1 (FALSE, shade region NOT containing the test point)

y < 10x +4

test (0,0) (Dashed boundary line)

0 < 10(0) + 4

0 < 4 (TRUE, shade region containing the test point)

y ≥ 8x (Solid Boundary line)

test (1, 0)

0 ≥ 8(1)

0 ≥ 8 (FALSE, shade region NOT containing the test point)

35.

36.

37.


y > -1/2x - 4

test (0, 0) (Dashed boundary line)

0 > -1/2(0) - 4

0 > -4 (TRUE, shade region containing the test point)

-3y < -9x + 3y > 3x – 1 (Dashed boundary line)

test (0, 0)

0 > 3(0) - 1

0 > -1 (TRUE, shade region containing the test point)

6x – 4y < -126x < 4y – 126x +12 < 4y3/2x +3 < yy > 3/2x +3 (Dashed boundary Line)

test (0, 0)

0 > 3/2(0) + 3

0 > 3 (FALSE, shade region NOT containing the test point)

38.

39.

40. Part A5 x+3 y>150, (x: smoothie, y: soft pretzel)Part B


16x + 6y > 36-16x -16x6y > -16x + 36y > -8/3x + 6 (Dashed boundary line)

test (0, 0)

0 > -8/3(0) + 6


y ≥ 6/5x -8 (Solid boundary line)

test (0, 0)

0 ≥ 6/5(0) - 8

0 ≥ -8 (TRUE, shade region containing the test point)

(Dashed boundary line)

Using the intercepts method:set x=0, y=50 -- y-intercept (0, 50)set y=0, x=30 – x-intercept (30, 0)

test (0, 0)

5(0) +3(0) > 150


Part CMultiple Answers ex: (25, 25) (Or, choose any point with coordinates in the shaded region)

41. Part A6 x+10 y≥1450 Part B

Part CA, C, and E

42. Part A6.50 x+7 y≤45 Part B

Part CB and E

HOMEWORK

43.


44.

45.

46.


y ≥ -4 (Solid boundary line)

test (0, 0)


x + 4y < 8-x - x4y < -x + 8 y < -1/4x + 2 (Dashed Boundary Line)

test (0, 0)

0 < -1/4(0) + 2

0 < 2 (TRUE, shade region containing the test point)

-5x + 4 y ≥ -24+5x +5x4y ≥ 5x – 24y ≥ 5/4x – 6 (Solid Boundary Line)

test (0, 0)

0 ≥ 5/4(0) – 6


47.

48.


y ≤ 3/5x +5 (Solid Boundary Line)

test (0, 0)

0 ≤ 3/5(0) +5

0 ≤ 5 (TRUE, shade region containing the test point)

2x + 3y < -15-2x -2x3y < -2x – 15y < -2/3x – 5 (Dashed Boundary Line)

test (0, 0)

0 < -2/3(0) – 5

0 < -5 (FALSE, shade region NOT containing the test point)

y > -2x +7 (Dashed Boundary line)

test (0, 0)

0 > -2(0) + 7


49.

50.

51. Part A5x+10y ≥ 150 (x: running, y: rollerblading)Part B


y ≤ 4/9x – 6 ( Solid Boundary line)

test (0, 0)

0 ≤ 4/9(0) – 6

0 ≤ -6 (FALSE, shade region NOT containing the test point)

-x + 3y < -12+x +x3y < x – 12y < 1/3x – 4 (Dashed Boundary line)

test (0, 0)

0 < 1/3(0) - 4

0 < -4 (FALSE, shade region NOT containing the test point)

(Solid boundary line)

Using the intercepts method:set x=0, y=15 -- y-intercept (0, 15)set y=0, x=30 – x-intercept (30, 0)

test (0, 0)

5(0) +10(0) ≥ 150

0 ≥ 150 (FALSE, shade region NOT containing the test point)

Part CMultiple Answers ex: (12,15) (or, choose any point with coordinates in the shaded region)

52. Part A9.50 x+15 y≥600 Part B

Part CA and D

53. Part A3.5 x+2.5 y<45 Part B

Part CB, C, and D

54.

55.

56.

57. _


58.

59. Part A2 x+2 y ≤100 x≥24 , y ≥12

Part BA and D

Part Cy ≤20, therefore the maximum width is 20 feetPart D

y ≤16 23 , therefore the maximum width is 16

feet

60. Part A6 x+10 y≥1850 x+2 y ≤350

Part BC and EPart C65 couples tickets need to be soldPart D100 individual tickets

61.


62.

63.

64.

(Parallel Lines)

65.

66. Part Ax+ y≥120 1.70 x+1.30 y ≤200

Part BB and DPart C50 lb. of avocadosPart D110 lb. of mangoes

67. Part Ax+ y≤42 8 x+15 y≥420


Part B

A and EPart C27 hours of baby sittingPart D30 hours of babysitting

Solving and Graphing Linear Inequalities Review Answer key1. d2. b3. b4. a and e5. c, e, and f

6. d7. b8. a9. d10. d

11. 3x + 2 < 0

12. ¼ x – 3/5 ≥ 2/3

13. 5x – 4 ≥ 6 and 7x + 11 < 32

14. 22 ≥ 2(2m – 1) or 5 – 3m ≤ -13

15. 7x + 4 < 18


16. 3x + y > 1

17. y < -1/9x – 1

18. Student solutions will vary. Sample Answers: 2x + 3 ≤ y x + y ≥ 1

19. Student solutions will vary. Sample answers: 9x – 38 > -2 x + y > 2

20. Student solutions will vary. Sample answers: 2x + 6 < 9 x < 1.5

21. Student solutions will vary. Sample answers: -5x – 1 ≤ 20 x ≥ -4.2

22. Student solutions will vary. Sample answer: 3x + 1 > 4 and 7x – 2 < 12

23. x<75 ° F∨x>90 ° F

24. y > x

y ≥ −12

x – 6

25. Part Ax≥3(22) Part Bx≥66; 66 is the minimum number of players required

26. Part A2x + 3.50y ≥ 1000x + y ≤ 400


Part B

Part CAnswers will varyPossible solutions: (50, 325) (200, 200) (0, 300)Part DBy selling 200 hot dogs and 200 hamburgers, the restaurant will make enough to meet their goal of $1000, by $100 (1,100 – 1,000 = 100).


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