Graphing and Solving Linear Inequalities in Real Life

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 an inequality to represent the number of classes they can attend. What is the graphical representation of this inequality?

• x ≤ 12

• x ≤ 14

• x ≤ 20

• x ≤ 10

A farmer has 200 feet of fencing to create a rectangular pen for his sheep. If the length of the pen is represented by x and the width by y, write an inequality that represents the area of the pen being less than or equal to 1000 square feet. How would you graph this inequality?

• x + y ≤ 200 and xy ≤ 500

• x + y < 100 and xy < 1000

• x + y ≤ 100 and xy ≤ 1000

• x + y = 100 and xy = 1000

A school is planning a field trip and has a budget of $500. The cost per student is $20. Write an inequality to represent the maximum number of students that can attend the trip. How can you interpret this solution graphically?

• x < 25

• x ≤ 20

• x ≥ 30

• x ≤ 25

A concert venue has a maximum capacity of 300 people. If tickets are sold for $15 each, write an inequality to represent the total revenue generated from ticket sales being less than or equal to $4500. How would you graph this situation?

• 20x ≤ 4500

• 10x ≤ 4500

• 15x < 4500

• 15x ≤ 4500

A bakery sells cupcakes for $3 each and cookies for $2 each. If the bakery wants to make at least $100 in one day, write an inequality to represent the number of cupcakes (x) and cookies (y) sold. How can you interpret the solution graphically?

• x + y ≥ 50

• 3x + 2y ≤ 100

• 4x + y ≥ 100

• 3x + 2y ≥ 100

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 an inequality to represent the number of miles they can drive. What does the graph of this inequality look like?

• m ≤ 250

• m ≤ 200

• m ≤ 300

• m ≤ 150

A charity event aims to raise at least $2000. If each ticket sold is $25, write an inequality to represent the number of tickets (x) that need to be sold. How can you represent this graphically?

• x < 80

• 25x < 2000

• x ≤ 80

• 25x ≥ 2000, or x ≥ 80

A student has a budget of $60 to spend on school supplies. If notebooks cost $5 each and pens cost $2 each, write an inequality to represent the total cost of supplies. How would you graph this situation?

• 5x + 2y < 60

• 10x + y <= 60

• 3x + 4y <= 60

• 5x + 2y <= 60

A local restaurant offers a special deal where a meal costs $10 and a drink costs $2. If a customer wants to spend no more than $30, write an inequality to represent the number of meals (x) and drinks (y) they can order. How can you interpret this graphically?

• 10x + 2y < 30

• 5x + 3y ≤ 30

• 10x + 2y ≤ 30

• 15x + y ≤ 30

A sports team has a budget of $1500 for new uniforms. If each uniform costs $75, write an inequality to represent the maximum number of uniforms that can be purchased. How would you graph this inequality?

• x ≤ 15

• x ≥ 25

• x ≤ 20

• x < 20