Mastering Inequalities: Writing & Graphing Challenges

A local bakery sells cupcakes for $2 each. They want to sell at least 50 cupcakes to break even. Write an inequality to represent the number of cupcakes they need to sell. What does the graph look like?

• x > 50

• x >= 50

• x < 50

• x <= 50

A school is planning a field trip and needs to raise at least $300. If each student contributes $15, how many students are needed? Write the inequality and sketch the graph.

• 20

• 30

• 15

• 25

A gym has a maximum capacity of 100 members. If there are currently 75 members, write an inequality to represent how many more members can join. Show this on a graph.

• x < 25

• x ≥ 50

• x ≤ 25

• x = 30

A farmer has a budget of $500 to buy seeds. If each packet of seeds costs $25, write an inequality to represent the maximum number of packets he can buy. Illustrate this with a graph.

• x < 20

• x <= 20

• x >= 20

• x <= 25

A concert venue can hold a maximum of 200 people. If 150 tickets have already been sold, write an inequality to show how many more tickets can be sold. Graph this situation.

• x = 200

• x ≤ 50

• x ≥ 150

• x < 50

A student needs to score at least 70% on a test to pass. If the test has 50 questions, write an inequality to represent the minimum number of questions they need to answer correctly. Show this on a graph.

• x >= 25

• x >= 40

• x >= 50

• x >= 35

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 for the number of miles they can drive. Graph this situation.

• m ≤ 75

• m ≤ 50

• m ≤ 100

• m ≤ 120

A charity event aims to raise at least $1,000. If each ticket sold is $20, write an inequality to represent the number of tickets that need to be sold. Illustrate this with a graph.

• 20x < 1000, x < 50

• 20x ≥ 1000, x ≥ 50

• 10x ≥ 1000, x ≥ 100

• 25x ≥ 1000, x ≥ 40

A store has a sale where customers can buy at most 5 items to get a discount. Write an inequality to represent this situation and sketch the graph.

• x ≤ 5

• x ≥ 5

• x = 5

• x < 5

A student needs to complete at least 15 hours of community service to graduate. If they have completed 8 hours, write an inequality to show how many more hours they need. Graph this situation.

• x < 7

• x >= 7

• x > 7

• x <= 7