Mastering Linear Inequalities: Graphing & Interpreting

A local bakery sells cupcakes for $2 each. They want to make at least $100 in sales. Write an inequality to represent the number of cupcakes, x, they need to sell. Graph the inequality and interpret the solution.

• x ≥ 50

• x > 50

• x ≤ 50

• x < 50

A school is planning a field trip and has a budget of $500. Each student ticket costs $15. Write an inequality to represent the maximum number of students, s, that can attend. Graph the inequality and explain what the graph indicates about the number of students.

• s <= 25

• s <= 30

• s <= 40

• s <= 33

A gym charges a monthly fee of $30 plus $5 for each class attended. If a member wants to spend no more than $100 in a month, write an inequality for the number of classes, c, they can attend. Graph the inequality and describe the solution.

• c ≤ 10

• c ≤ 20

• c ≤ 14

• c ≤ 5

A farmer has 200 acres of land and wants to plant corn and wheat. Each acre of corn requires 1.5 hours of labor, and each acre of wheat requires 2 hours. If the farmer has 300 hours of labor available, write an inequality for the acres of corn, c, and wheat, w. Graph the inequality and interpret the feasible region.

• c + w ≥ 200 and 1.5c + 2w ≥ 300

• c + w ≤ 200 and 1.5c + 2w ≤ 300

• c + w ≤ 150 and 1.5c + 2w ≤ 250

• c + w ≤ 200 and 1.5c + 2w = 300

A concert venue has a seating capacity of 800. If tickets are sold for $20 each, write an inequality to represent the number of tickets, t, that can be sold. Graph the inequality and explain what the graph reveals about ticket sales.

• t = 800

• t <= 800

• t >= 800

• t < 800

A car rental company charges a flat fee of $50 plus $0.25 per mile driven. If a customer wants to spend no more than $100, write an inequality for the number of miles, m, they can drive. Graph the inequality and interpret the results.

• m < 100

• m ≥ 200

• m ≤ 150

• m ≤ 200

A clothing store has a sale where each shirt costs $15. If a customer wants to buy shirts without spending more than $75, write an inequality for the number of shirts, s, they can purchase. Graph the inequality and explain the solution.

• s ≤ 10

• s < 5

• s ≤ 3

• s ≤ 5

A restaurant has a special where each meal costs $12. If a family wants to spend no more than $60 on meals, write an inequality for the number of meals, m, they can order. Graph the inequality and describe the solution.

• m ≤ 4

• m ≤ 6

• m < 5

• m ≤ 5

A local gym has a promotion where each membership costs $40 plus $10 for each class. If a member wants to spend no more than $100, write an inequality for the number of classes, c, they can take. Graph the inequality and interpret the results.

• c ≤ 6

• c ≤ 10

• c ≤ 4

• c ≤ 8