Exploring Inequalities: Graphs and Solutions in Real Life

A local gym has a membership fee of $30 per month. They also charge an additional fee for classes. If the total cost for a month is represented by the inequality y > 30 + 10x, where x is the number of classes taken, what does the graph of this inequality look like?

• The graph is a solid line with shading below the line y = 30 + 10x.

• The graph is a dashed line with shading above the line y = 30 + 10x.

• The graph is a dashed line with shading below the line y = 30 + 10x.

• The graph is a solid line with shading above the line y = 30 + 10x.

A farmer has a budget of $200 to spend on seeds. If each type of seed costs $15, write an inequality that represents the number of seed types he can buy. What would the graph of this inequality show?

• x < 13

• x ≤ 10

• x ≥ 15

• x ≤ 13

A school is planning a field trip and has a budget of $500. If each student pays $25, write an inequality to represent the maximum number of students that can attend. How would you graph this inequality?

• x ≤ 15

• x ≤ 25

• x ≤ 10

• x ≤ 20

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write an inequality to represent the total cost y for driving x miles. What does the graph of this inequality indicate about the costs?

• y < 50 + 0.20x

• y >= 50 + 0.20x

• y = 50 + 0.20x

• y <= 50 + 0.20x

A concert venue has a maximum capacity of 300 people. If tickets are sold for $20 each, write an inequality to represent the total revenue y from selling x tickets. How would you graph this inequality?

• y >= 20x, x <= 250

• y < 20x, x > 300

• y <= 20x, x <= 300

• y = 20x, x < 300

A bookstore has a sale where each book costs $8. If a customer has $50 to spend, write an inequality to represent the number of books x they can buy. What does the graph of this inequality reveal?

• 8x < 50, x < 6

• 8x >= 50, x >= 6

• 8x = 50, x = 6

• 8x <= 50, x <= 6

A pizza shop sells pizzas for $12 each. If a customer wants to spend no more than $60, write an inequality to represent the number of pizzas x they can buy. How would you graph this inequality?

• 12x < 60, x < 5

• 12x ≤ 60, x ≤ 5

• 12x ≤ 50, x ≤ 4

• 12x ≥ 60, x ≥ 5

A charity event aims to raise at least $1,000. If each ticket sold is $25, write an inequality to represent the number of tickets x that need to be sold. What does the graph of this inequality show about the fundraising goal?

• 25x >= 1000, or x >= 40

• x < 40

• 25x < 1000

• x <= 40

A local bakery sells cupcakes for $3 each. If they want to make at least $150 in a day, write an inequality to represent the number of cupcakes x they need to sell. How would you graph this inequality?

• x > 50

• 3x ≤ 150

• x < 50

• 3x ≥ 150 or x ≥ 50

A student has a part-time job and earns $15 per hour. If they want to save at least $200 for a new bike, write an inequality to represent the number of hours x they need to work. What does the graph of this inequality indicate about their savings?

• 15x < 200

• 15x ≥ 200, x ≥ 14

• 15x = 200

• x < 14