Graphing Inequalities: Real-Life Scenarios for 8th Graders

1. Sarah has twice as many apples as Tom. If Tom has x apples, write an inequality to represent the situation if Sarah has at least 10 apples. Solve for x and graph the solution on a number line.

• x >= 5

• x > 10

• x = 7

• x < 5

2. A movie theater charges $8 per ticket. If you buy x tickets, the total cost is less than $50. Write and solve the inequality to find the maximum number of tickets you can buy. Graph your solution.

• 7

• 6

• 5

• 10

3. A store sells notebooks for $3 each and pens for $2 each. If you buy x notebooks and y pens, and you want to spend no more than $20, write an inequality and solve for y in terms of x. Graph the solution on a number line.

• y = 12 - 1.2x

• y ≤ 5 - 2x

• y ≤ 10 - 1.5x

• y ≥ 15 - 0.5x

4. The sum of three times a number and 5 is greater than or equal to 20. Write the inequality, solve for the number, and represent the solution on a number line.

• x <= 0

• x >= 5

• x < 5

• x > 10

5. A car rental company charges a flat fee of $50 plus $0.25 per mile driven. If you want to spend no more than $100, write an inequality to represent the miles driven and solve for the maximum miles. Graph your solution.

• 200 miles

• 300 miles

• 150 miles

• 250 miles

6. A gardener has x square feet of garden space. If he wants to plant flowers that require 2 square feet each and vegetables that require 3 square feet each, and he has a total of 30 square feet, write an equation and solve for the number of flowers he can plant. Graph the solution.

• 15

• 5

• 20

• 10

7. A school is planning a field trip and has a budget of $500. If each student pays $25, write an inequality to find the maximum number of students that can go on the trip. Solve and graph the solution on a number line.

• x ≤ 10

• x ≤ 20

• x ≤ 25

• x ≤ 15

8. A recipe requires 2 cups of flour and 3 cups of sugar. If you have x cups of flour and want to make at least 5 batches, write an inequality and solve for x. Graph the solution on a number line.

• x = 15

• x < 10

• x <= 5

• x >= 10

9. A bike shop sells bikes for $150 each. If you want to buy x bikes and spend no more than $600, write and solve the inequality for x. Graph your solution.

• x = 3

• x < 4

• x ≤ 5

• x ≤ 4

10. A student scored 75% on a test. If the test had x questions and he answered at least 30 questions correctly, write an inequality to represent this situation. Solve for x and graph the solution on a number line.

• x < 30

• x = 50

• x ≥ 40

• x ≤ 35