Mastering Linear Inequalities and Boundary Lines Challenge

A local 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 and graph the inequality that represents the number of classes they can attend.

• x ≤ 10

• x ≤ 20

• x ≤ 14

• x ≤ 12

A farmer has 200 feet of fencing to create a rectangular pen for his sheep. If the length of the pen is to be at least twice the width, write and graph the inequality that represents the possible dimensions of the pen.

• 0 < w <= 25, l >= w; l + w = 200.

• 0 < w <= 40, l >= 4w; l + w = 80.

• 0 < w <= 33.33, l >= 2w; l + w = 100.

• 0 < w <= 50, l >= 3w; l + w = 100.

A school is planning a field trip and has a budget of $500. The cost per student is $20, and they want to ensure that the total cost does not exceed the budget. Write and graph the inequality for the number of students that can attend the trip.

• x ≤ 20

• x ≤ 30

• x ≤ 25

• x ≤ 15

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer wants to keep their total cost under $100, write and graph the inequality that shows the maximum number of miles they can drive.

• m < 300

• m < 200

• m < 150

• m < 250

A concert venue has a maximum capacity of 500 people. If they want to sell tickets at $15 each, but also want to reserve 100 seats for VIP guests, write and graph the inequality that represents the number of general admission tickets they can sell.

• x ≤ 500

• x ≤ 450

• x ≤ 400

• x ≤ 300

A bakery sells cupcakes for $3 each and cookies for $2 each. If a customer wants to spend no more than $30, write and graph the inequality that represents the combination of cupcakes and cookies they can buy.

• 4x + 3y ≤ 30

• 3x + 2y ≤ 30

• 2x + 5y ≤ 30

• 3x + 2y < 30

A student is saving money for a new laptop that costs $800. If they save $50 each month, write and graph the inequality that shows how many months it will take to save enough money, considering they want to save for at least 10 months.

• m < 16

• m = 10

• m >= 16

• m <= 15

A clothing store has a sale where jeans are $40 each and shirts are $20 each. If a customer wants to spend no more than $200, write and graph the inequality that represents the maximum number of jeans and shirts they can buy.

• 30x + 10y ≤ 200

• 50x + 25y ≤ 200

• 40x + 20y ≤ 200

• 20x + 30y ≤ 200

A charity event aims to raise at least $1,000. If they charge $10 per ticket, write and graph the inequality that represents the minimum number of tickets they need to sell to meet their goal.

• x < 100

• x >= 100

• x <= 100

• x > 100

A tech company produces gadgets and has a production limit of 300 units per day. If they want to produce at least 50 more gadgets than they did the previous day, write and graph the inequality that represents their production for today.

• x >= 50 + y and x >= 300

• x >= 50 + y and x <= 300

• x > 50 + y and x < 300

• x <= 50 + y and x >= 0