Mastering Inequalities: Solving & Graphing Challenges

1. Sarah has at least 15 apples. If she gives away x apples, write an inequality to represent how many apples she has left. Solve for x.

• x >= 15

• x = 15

• x < 15

• x <= 15

2. A movie theater has a maximum capacity of 200 people. If there are currently y people in the theater, write an inequality to show how many more people can enter. Solve for y.

• y < 200

• y = 200

• y > 200

• y ≤ 200

3. Tom needs to score more than 75 points on his test to pass. If he has already scored z points, write an inequality to represent this situation. Solve for z.

• z > 75

• z ≥ 75

• z = 75

• z < 75

4. A store sells notebooks for $3 each. If you want to spend no more than $30, write an inequality to represent how many notebooks you can buy. Solve for the number of notebooks.

• x ≤ 10

• x ≤ 5

• x ≤ 15

• x ≤ 20

5. A runner wants to complete a race in less than 2 hours. If she has already run for t hours, write an inequality to show how much time she has left. Solve for t.

• t < 2

• x < 2 - t

• t > 2

• t = 2

6. A class needs at least 12 students to go on a field trip. If x students have signed up, write an inequality to represent the situation. Solve for x.

• x < 12

• x >= 12

• x <= 12

• x = 12

7. A recipe requires no more than 4 cups of flour. If you have y cups of flour, write an inequality to show how much more you can use. Solve for y.

• y <= 4, additional flour = 4 - y

• y >= 4, additional flour = 0

• y < 4, additional flour = y - 4

• y = 4, additional flour = 4

8. A car can travel at a speed of no more than 60 miles per hour. If it has already traveled at a speed of s miles per hour, write an inequality to represent the maximum speed. Solve for s.

• s >= 60

• s = 60

• s <= 60

• s < 60

9. A gardener wants to plant at least 20 flowers. If he has already planted f flowers, write an inequality to represent how many more he can plant. Solve for f.

• x < 20 + f

• x = 20 - f

• x <= 20 - f

• x >= 20 - f

10. A student needs to read more than 100 pages to finish a book. If he has read r pages, write an inequality to represent how many more pages he needs to read. Solve for r.

• r > 100

• r = 100

• r ≤ 100

• r < 100