Mastering Graphing and Solving Linear Inequalities

A school is planning a field trip and has a budget of $500. Each ticket costs $25. Write a linear inequality to represent the number of tickets (t) they can buy. Graph the inequality.

• 25t >= 500

• t <= 20

• 25t <= 500

• t > 20

Maria has $120 to spend on books. Each book costs $15. Write a linear inequality to show how many books (b) she can buy. Solve the inequality and graph it.

• b <= 8

• b = 5

• b < 8

• b >= 10

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 a linear inequality for the number of classes (c) they can attend. Graph the inequality.

• c ≤ 14

• c ≤ 10

• c ≤ 5

• c ≤ 20

A farmer has 200 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 1 hour. If the farmer has 300 hours of labor available, write a linear inequality for the acres of corn (c) and wheat (w) he can plant. Solve and graph the inequality.

• c + w ≤ 200 and 2c + w ≤ 300

• c + w ≤ 200 and 2c + w ≤ 400

• c + w ≥ 200 and 2c + w ≥ 300

• c + w ≤ 150 and 2c + w ≤ 250

A concert hall has a seating capacity of 800. If tickets are sold for $20 each, write a linear inequality to represent the number of tickets (t) that can be sold without exceeding capacity. Graph the inequality.

• t >= 800

• t <= 800

• t < 800

• t = 800

A company produces x units of a product at a cost of $5 per unit. If the total cost must not exceed $200, write a linear inequality for the number of units produced. Solve and graph the inequality.

• 5x < 200; x < 40

• 5x ≤ 200; x ≤ 40

• 5x = 200; x = 40

• 5x ≥ 200; x ≥ 40

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer wants to spend no more than $100, write a linear inequality for the number of miles (m) they can drive. Solve and graph the inequality.

• m ≤ 250

• m ≤ 200

• m ≤ 300

• m ≤ 150

A local bakery can produce a maximum of 300 loaves of bread in a day. If they produce white bread (w) and whole grain bread (g), write a linear inequality to represent the total loaves produced. Graph the inequality.

• w + g < 300

• w + g ≤ 300

• w + g = 300

• w + g ≥ 300

A student has a part-time job and earns $10 per hour. If they want to save at least $200 for a new bike, write a linear inequality for the number of hours (h) they need to work. Solve and graph the inequality.

• h > 25

• h = 15

• h < 20

• h >= 20

A charity event has a goal of raising at least $1,000. If each ticket sold is $25, write a linear inequality to represent the number of tickets (t) that need to be sold. Solve and graph the inequality.

• t > 40

• t >= 40

• t <= 40

• t < 40