Mastering Inequalities: Isolate Variables & Check Solutions

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 check your solution.

• x >= 5

• x < 5

• x <= 3

• x = 10

2. A store sells notebooks for $2 each and pens for $1 each. If the total cost of notebooks and pens is less than $20, write an inequality to represent the situation if the number of notebooks is n and the number of pens is p. Solve for p in terms of n and check your solution.

• p < 20 - 2n

• p < 20 - n

• p > 20 - 2n

• p < 10 - 2n

3. A car rental company charges a flat fee of $30 plus $0.50 per mile driven. If a customer wants to spend no more than $60, write an inequality to represent the situation. Solve for the number of miles driven and check your solution.

• x < 60

• x ≥ 60

• x ≤ 60

• x = 60

4. Emily is saving money for a new bike that costs $150. If she saves $15 each week, write an inequality to represent how many weeks, w, it will take her to save enough money. Solve for w and check your solution.

• w >= 10

• w <= 15

• w < 10

• w > 10

5. A gardener has x square feet of garden space. If he wants to plant flowers that require 3 square feet each and vegetables that require 2 square feet each, write an inequality if he wants to plant at least 10 flowers and 5 vegetables. Solve for x and check your solution.

• x >= 20

• x >= 50

• x >= 30

• x >= 40

6. A school is planning a field trip and has a budget of $500. If each student pays $25 and there are s students, write an inequality to represent the situation. Solve for s and check your solution.

• s < 20

• s >= 25

• s = 15

• s <= 20

7. A recipe requires 2 cups of flour and 3 cups of sugar. If you have x cups of flour and y cups of sugar, write an inequality to represent the situation if you want to make at least 5 batches of the recipe. Solve for y in terms of x and check your solution.

• y >= 15

• y <= 20

• y < 15

• y >= 10

8. A concert hall has a seating capacity of 200. If tickets are sold for $15 each and the total revenue must be at least $2,000, write an inequality to represent the situation. Solve for the number of tickets sold and check your solution.

• At least 134 tickets must be sold.

• At least 100 tickets must be sold.

• At least 150 tickets must be sold.

• At least 200 tickets must be sold.

9. A factory produces x toys per hour. If the factory needs to produce at least 500 toys in a day (8 hours), write an inequality to represent the situation. Solve for x and check your solution.

• x > 70

• x <= 62

• x < 50

• x >= 63

10. A student scored 75% on a test with 40 questions. If the student wants to improve their score to at least 85%, write an inequality to represent the number of questions they need to answer correctly on a retake. Solve for the number of correct answers needed and check your solution.

• 40

• 30

• 38

• 34