Inequality Challenges: Solve & Graph for 8th Grade

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 >= 5

• x = 7

• x > 10

2. A concert hall has a seating capacity of 500. If tickets are sold for x dollars each, and the total revenue must be at least $3000, write an inequality and solve for x. Graph the solution on a number line.

• x < 6

• x ≥ 6

• x > 10

• x ≤ 5

3. A store sells pencils for 50 cents each and erasers for 75 cents each. If the total cost for pencils and erasers is less than $10, and you buy x pencils and y erasers, write an inequality and solve for x and y. Graph the solution.

• 25x + 50y < 500

• 50x + 75y < 1000

• 50x + 75y > 1000

• 100x + 75y < 1000

4. A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If you want to spend no more than $60, write an inequality to represent the miles driven and solve for x. Graph the solution on a number line.

• x ≤ 150

• x < 150

• x = 100

• x ≥ 200

5. Emily is saving money for a new bike that costs $150. If she saves x dollars each week, write an inequality to show how many weeks it will take her to save enough money if she has already saved $30. Solve for x and graph the solution.

• x = 120/w

• x >= 120/w

• x > 120/w

• x < 120/w

6. A farmer has 120 acres of land. He wants to plant corn and wheat, with corn taking 2 acres and wheat taking 3 acres per field. If he wants to plant at least 20 fields, write an inequality and solve for the number of fields of corn and wheat. Graph the solution.

• x + y <= 20, 2x + 3y = 120

• x >= 10, y >= 10, 2x + 3y = 100

• x >= 0, y >= 20 - x, 2x + 3y <= 120

• x <= 0, y <= 20 - x, 2x + 3y >= 120

8. A recipe requires 2 cups of flour and 3 cups of sugar. If you want to make at least 5 batches of the recipe, write an inequality for the total amount of flour and sugar needed. Solve for the amounts and graph the solution on a number line.

• F + S = 30

• F + S > 15

• F + S >= 25

• F + S <= 20

9. A gym charges a monthly fee of $40 plus $5 per class. If you want to spend no more than $100 in a month, write an inequality to represent the number of classes you can take. Solve for x and graph the solution.

• x ≤ 8

• x ≤ 15

• x ≤ 10

• x ≤ 12

10. A bookstore sells novels for $12 each and textbooks for $20 each. If you want to spend less than $100 on x novels and y textbooks, write an inequality and solve for x and y. Graph the solution on a number line.

• 10x + 15y < 100

• 5x + 25y < 100

• 12x + 20y < 100

• 12x + 10y < 100