Practice: Inequalities

Part A: Translating Words to Inequalities

Directions: Write each statement as an inequality using x as the variable.

1. x is less than 12

2. x is greater than or equal to 5

3. x is at most 20

4. x is at least 8

5. x is no more than 15

6. x is greater than -3

Part B: Solving One-Step Inequalities

Directions: Solve each inequality. Show your work.

7. x + 5 > 12

8. y - 3 < 8

9. 4n ≥ 24

10. m/3 ≤ 5

11. a + 9 ≤ 15

12. 5b > 35

Part C: Graphing Inequalities on Number Lines

Directions: Graph each inequality on the number line. Remember: use an open circle for < or >, and a closed circle for ≤ or ≥.

13. x > 2

←──-1──0──1──2──3──4──5──→

14. x ≤ 4

←──1──2──3──4──5──6──7──→

15. x ≥ -1

←──-3──-2──-1──0──1──2──3──→

16. x < 0

←──-3──-2──-1──0──1──2──3──→

Part D: Writing Inequalities from Graphs

Directions: Write the inequality shown by each graph.

17.

←──1──2──●──4──5──6──→

(Closed circle at 3, shaded left)

Inequality:

18.

←──0──1──○──3──4──5──→

(Open circle at 2, shaded right)

Inequality:

Part E: Identifying Solutions

Directions: Circle ALL values that are solutions to the given inequality.

19. Which values are solutions to x > 4?

3 4 4.5 5 10 0

20. Which values are solutions to y ≤ 6?

6 7 5.9 -2 0 100

Part F: Word Problems

Directions: Write an inequality for each situation, then solve if needed.

21. You must be at least 13 years old to create a social media account. Write an inequality where a represents age.

Inequality:

22. The speed limit on a highway is at most 65 mph. Write an inequality where s represents speed.

Inequality:

23. Maya has $50 to spend at the mall. She already spent $18 on lunch. Write and solve an inequality to find how much more money (m) she can spend.

Inequality:

Solution:

24. A roller coaster requires riders to be more than 48 inches tall. Tomás is 42 inches tall. Write and solve an inequality to find how many more inches (h) he needs to grow.

Inequality:

Solution:

Challenge: Think About It!

25. Explain why x > 5 and x ≥ 5 have different graphs. What numbers are solutions to x ≥ 5 but NOT solutions to x > 5?

26. A movie theater charges $8 per ticket. You have $50. Write an inequality for the number of tickets (t) you can buy, then find the maximum number of tickets.

Maximum tickets: