Exploring Real-World Linear Inequalities and Graphing Skills

A local gym charges a monthly fee of $30 plus $5 for each class attended. If you want to spend no more than $100 a month, how many classes can you attend? Graph the inequality and interpret the solution.

• 12

• 16

• 10

• 14

A school is planning a field trip and has a budget of $500. The cost per student is $20. Write an inequality to represent the maximum number of students that can attend the trip. Graph the inequality and explain what the solution means.

• x < 25

• x ≤ 20

• x ≤ 25

• x ≤ 30

A farmer has 120 acres of land and wants to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 3 hours. If the farmer has a maximum of 240 hours of labor available, write and graph the inequality to show the possible combinations of corn and wheat that can be planted.

• x + y >= 120, 2x + 3y >= 240

• x + y <= 100, 2x + 3y <= 300

• x + y <= 120, 2x + 3y <= 240

• x + y = 120, 2x + 3y = 240

A concert venue can hold a maximum of 1,500 people. If tickets are sold for $20 each, how many tickets can be sold without exceeding the venue's capacity? Write the inequality, graph it, and interpret the solution.

• x < 1500

• x >= 1500

• x = 1500

• x <= 1500

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 3 hours of labor, and each Type B gadget requires 2 hours. If the company has 30 hours of labor available, write an inequality to represent the production limits. Graph the inequality and explain the implications of the solution.

• 3x + 2y ≥ 30

• 3x + 2y = 30

• 2x + 3y ≤ 30

• 3x + 2y ≤ 30

A pizza shop sells large pizzas for $15 each and small pizzas for $10 each. If the shop wants to make at least $200 in a day, write an inequality to represent the number of large and small pizzas that can be sold. Graph the inequality and interpret the solution.

• 5x + 10y ≥ 200

• 20x + 5y ≥ 200

• 15x + 10y ≥ 200

• 15x + 10y ≤ 200

A student has a budget of $50 to spend on school supplies. If notebooks cost $5 each and pens cost $2 each, write an inequality to represent the maximum number of notebooks and pens the student can buy. Graph the inequality and explain the solution.

• 5n + 2p <= 50

• 5n + 2p < 50

• 3n + 4p <= 50

• 10n + p <= 50

A charity event aims to raise at least $1,000. If each ticket sold is $25, how many tickets must be sold to meet the goal? Write the inequality, graph it, and interpret the solution.

• At least 30 tickets must be sold.

• At least 50 tickets must be sold.

• At least 20 tickets must be sold.

• At least 40 tickets must be sold.

A factory produces toys and games. Each toy requires 4 hours of work, and each game requires 2 hours. If the factory has 40 hours of work available, write an inequality to represent the production limits. Graph the inequality and explain the solution.

• 4x + 2y ≤ 40

• 3x + 2y ≤ 40

• 4x + 3y ≤ 40

• 2x + 4y ≤ 40

A bookstore has a sale where each book costs $8. If a customer wants to spend no more than $40, how many books can they buy? Write the inequality, graph it, and interpret the solution.

• 6

• 7

• 4

• 5