Real-Life Inequalities: Graphing and Solving Challenges

1. A school is planning a field trip and needs at least 30 students to sign up. If 5 students have already signed up, write an inequality to represent the number of additional students needed. Graph the inequality on a number line.

• x > 25

• x < 25

• x <= 30

• x >= 25

2. A local gym charges a monthly fee of $40 plus $5 for each class attended. If a member wants to spend no more than $100 in a month, write an inequality to represent the number of classes they can attend. Solve the inequality and graph it.

• x ≤ 15

• x ≤ 12

• x ≤ 8

• x ≤ 10

3. A farmer has a budget of $200 to buy seeds. If each packet of seeds costs $15, write an inequality to represent the maximum number of packets he can buy. Solve the inequality and represent it on a graph.

• x <= 13

• x >= 14

• x = 15

• x < 13

4. A concert venue can hold a maximum of 500 people. If 150 tickets have already been sold, write an inequality to represent the number of tickets still available. Graph the inequality on a number line.

• x > 500

• x <= 350

• x < 350

• x >= 150

5. A student needs to score at least 75% on a test to pass. If the test has 20 questions, write an inequality to find the minimum number of questions the student must answer correctly. Solve and graph the inequality.

• 10

• 18

• 15

• 12

6. A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer wants to spend no more than $50, write an inequality to represent the maximum miles they can drive. Solve and graph the inequality.

• m ≤ 100

• m ≤ 90

• m ≤ 120

• m ≤ 80

7. A bakery sells cupcakes for $2 each. If a customer wants to spend less than $20, write an inequality to represent the maximum number of cupcakes they can buy. Solve the inequality and graph it.

• x < 5, maximum cupcakes = 4

• x < 8, maximum cupcakes = 7

• x < 15, maximum cupcakes = 14

• x < 10, maximum cupcakes = 9

8. A student is saving money for a new laptop that costs $600. If they currently have $150 and plan to save $50 each month, write an inequality to represent the number of months needed to save enough money. Solve and graph the inequality.

• x <= 10

• x > 8

• x < 9

• x >= 9

9. A charity event aims to raise at least $1,000. If they have already raised $450, write an inequality to represent the additional amount they need to raise. Solve the inequality and graph it.

• x >= 550

• x > 600

• x <= 450

• x < 550

10. A pet store has a limit of 10 pets per customer. If a customer already has 3 pets, write an inequality to represent the maximum number of additional pets they can adopt. Solve the inequality and graph it.

• x ≤ 5

• x ≤ 7

• x < 7

• x ≤ 10