Inequalities in Real Life: Write and Identify Boundaries

A store sells notebooks for $2 each. If you want to spend no more than $20, write an inequality to represent the number of notebooks you can buy. What is the boundary point?

• x ≤ 10; boundary point is 10

• x ≤ 15; boundary point is 15

• x < 10; boundary point is 9

• x ≤ 5; boundary point is 5

Maria has $50 to spend on books. Each book costs $8. Write an inequality to show how many books she can buy. Identify the boundary point.

• b < 6, boundary point is 5

• b <= 6, boundary point is 6

• b <= 7, boundary point is 7

• b >= 6, boundary point is 6

A gym charges a monthly fee of $30 plus $5 for each class attended. If you want to spend no more than $100 in a month, write an inequality for the number of classes you can attend. What is the boundary point?

• x ≤ 12, boundary point is 12

• x ≤ 20, boundary point is 20

• x ≤ 14, boundary point is 14

• x ≤ 10, boundary point is 10

A car rental company charges a flat fee of $40 plus $0.25 per mile driven. If you want to keep your total cost under $100, write an inequality for the number of miles you can drive. Identify the boundary point.

• m = 240

• m < 240

• m > 300

• m < 200

A concert ticket costs $15. If you want to buy tickets for your friends and spend no more than $75, write an inequality to represent the number of tickets you can purchase. What is the boundary point?

• 10x ≤ 75; boundary point is 7 tickets.

• 20x ≤ 75; boundary point is 3 tickets.

• 15x < 75; boundary point is 4 tickets.

• 15x ≤ 75; boundary point is 5 tickets.

A farmer has a budget of $200 to buy seeds. Each packet of seeds costs $12. Write an inequality to represent how many packets he can buy. Identify the boundary point.

• 12x <= 200; boundary point is 16.67

• 12x >= 200; boundary point is 20

• 12x < 200; boundary point is 16

• 12x = 200; boundary point is 15

A school is planning a field trip and has a budget of $500. Each student’s ticket costs $25. Write an inequality to determine how many students can go on the trip. What is the boundary point?

• x ≥ 20; boundary point is 20.

• x ≤ 20; boundary point is 20.

• x < 20; boundary point is 19.

• x ≤ 25; boundary point is 25.

A video game costs $60. If you want to buy it and still have at least $20 left, write an inequality to represent how much money you need. Identify the boundary point.

• x <= 100

• x < 60

• x > 80

• x >= 80

A family wants to spend no more than $150 on groceries. If they plan to buy fruits that cost $3 each, write an inequality to represent how many fruits they can buy. What is the boundary point?

• 2x ≤ 150; boundary point is 75 fruits.

• 4x ≤ 150; boundary point is 37.5 fruits.

• x ≤ 150; boundary point is 150 fruits.

• 3x ≤ 150; boundary point is 50 fruits.

A local charity is collecting donations. They want to raise at least $1,000. If each donation is at least $50, write an inequality to represent the minimum number of donations needed. Identify the boundary point.

• 60x <= 1000; boundary point: x = 16.67

• 50x >= 1000; boundary point: x = 20

• 30x >= 1000; boundary point: x = 33.33

• 40x > 1000; boundary point: x = 25