Mastering Linear Inequalities: 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 ≤ 12

• x ≤ 14

• x ≤ 20

• x ≤ 10

A farmer has 200 feet of fencing to create a rectangular pen for 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 <= 33.33, l >= 2w, l + w = 100

• 0 < w < 40, l <= w, l + w = 150

• 0 < w <= 25, l >= 3w, l + w = 100

• 0 < w < 50, l <= 2w, l + w = 200

A school is planning a field trip and has a budget of $500. The cost per student is $20. Write and graph the inequality that shows the maximum number of students that can attend the trip without exceeding the budget.

• x ≤ 25

• x ≤ 20

• x ≤ 30

• x ≤ 15

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 and graph the inequality that represents the maximum number of miles they can drive.

• m <= 300

• m <= 250

• m <= 200

• m <= 150

A concert venue has a seating capacity of 500. If tickets are sold for $15 each, write and graph the inequality that represents the maximum number of tickets that can be sold to stay within the capacity limit.

• x >= 500

• x < 500

• x = 500

• x <= 500

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 maximum number of cupcakes and cookies they can buy, assuming they buy at least 5 cupcakes.

• 3x + 2y ≤ 30, x ≥ 5

• 4x + 3y ≤ 30, x ≥ 5

• 3x + 2y ≤ 30, x ≤ 5

• 3x + 2y ≤ 25, x ≥ 5

A student has a budget of $40 to spend on school supplies. If notebooks cost $5 each and pens cost $2 each, write and graph the inequality that represents the maximum number of notebooks and pens they can buy, given they want at least 3 notebooks.

• 4x + 3y ≤ 40, x ≥ 3

• 5x + 2y ≤ 30, x ≥ 2

• 5x + 2y ≤ 50, x ≥ 4

• 5x + 2y ≤ 40, x ≥ 3

A local theater has a maximum of 300 seats. If tickets are sold for $10 each, write and graph the inequality that represents the maximum number of tickets that can be sold without exceeding the seating capacity.

• x >= 300

• x <= 300

• x = 300

• x < 300

A charity event aims to raise at least $1,000. If each ticket sold is $25, write and graph the inequality that represents the minimum number of tickets that need to be sold to meet the fundraising goal.

• x > 40

• x <= 40

• x < 40

• x >= 40

A pet store has a limit of 50 animals that can be housed. If they currently have 30 dogs and each dog takes up 1 space, write and graph the inequality that represents the maximum number of cats they can add to the store.

• c <= 10

• c <= 20

• c <= 15

• c <= 25