1 of 22

UST Middle School Pre-Algebra Challenge

Week 6 — Inequalities

Focus: Graphing and solving simple inequalities

2 of 22

Weekly Format

Week 6

Part A — 15 Multiple Choice

Part B — 15 Fill in the Blank

Part C — 15 Word / Open-Response Problems

Part D — 5 Challenge Problems

Answers and step-by-step explanations are provided at the end.

3 of 22

Part A — Multiple Choice

Questions 1–5

1. Which number satisfies x > 3? A) 2 B) 3 C) 4 D) 0

2. Which number satisfies x > 4? A) 3 B) 4 C) 5 D) 0

3. Which number satisfies x > 5? A) 4 B) 5 C) 6 D) 0

4. Which number satisfies x > 6? A) 5 B) 6 C) 7 D) 0

5. Which number satisfies x > 7? A) 6 B) 7 C) 8 D) 0

4 of 22

Part A — Multiple Choice

Questions 6–10

6. Which number satisfies x > 8? A) 7 B) 8 C) 9 D) 0

7. Which number satisfies x > 9? A) 8 B) 9 C) 10 D) 0

8. Which number satisfies x > 10? A) 9 B) 10 C) 11 D) 0

9. Which number satisfies x > 11? A) 10 B) 11 C) 12 D) 0

10. Which number satisfies x > 12? A) 11 B) 12 C) 13 D) 0

5 of 22

Part A — Multiple Choice

Questions 11–15

11. Which number satisfies x > 13? A) 12 B) 13 C) 14 D) 0

12. Which number satisfies x > 14? A) 13 B) 14 C) 15 D) 0

13. Which number satisfies x > 15? A) 14 B) 15 C) 16 D) 0

14. Which number satisfies x > 16? A) 15 B) 16 C) 17 D) 0

15. Which number satisfies x > 17? A) 16 B) 17 C) 18 D) 0

6 of 22

Part B — Fill in the Blank

Questions 16–20

16. Solve x + 1 ≤ 3. x ≤ ___.

17. Solve x + 2 ≤ 6. x ≤ ___.

18. Solve x + 3 ≤ 9. x ≤ ___.

19. Solve x + 4 ≤ 12. x ≤ ___.

20. Solve x + 5 ≤ 15. x ≤ ___.

7 of 22

Part B — Fill in the Blank

Questions 21–25

21. Solve x + 6 ≤ 18. x ≤ ___.

22. Solve x + 7 ≤ 21. x ≤ ___.

23. Solve x + 8 ≤ 24. x ≤ ___.

24. Solve x + 9 ≤ 27. x ≤ ___.

25. Solve x + 10 ≤ 30. x ≤ ___.

8 of 22

Part B — Fill in the Blank

Questions 26–30

26. Solve x + 11 ≤ 33. x ≤ ___.

27. Solve x + 12 ≤ 36. x ≤ ___.

28. Solve x + 13 ≤ 39. x ≤ ___.

29. Solve x + 14 ≤ 42. x ≤ ___.

30. Solve x + 15 ≤ 45. x ≤ ___.

9 of 22

Part C — Word / Open Response

Questions 31–35

31. A ride requires riders to be at least 49 inches tall. Write an inequality for height h.

32. A ride requires riders to be at least 50 inches tall. Write an inequality for height h.

33. A ride requires riders to be at least 51 inches tall. Write an inequality for height h.

34. A ride requires riders to be at least 52 inches tall. Write an inequality for height h.

35. A ride requires riders to be at least 53 inches tall. Write an inequality for height h.

10 of 22

Part C — Word / Open Response

Questions 36–40

36. A ride requires riders to be at least 54 inches tall. Write an inequality for height h.

37. A ride requires riders to be at least 55 inches tall. Write an inequality for height h.

38. A ride requires riders to be at least 56 inches tall. Write an inequality for height h.

39. A ride requires riders to be at least 57 inches tall. Write an inequality for height h.

40. A ride requires riders to be at least 58 inches tall. Write an inequality for height h.

11 of 22

Part C — Word / Open Response

Questions 41–45

41. A ride requires riders to be at least 59 inches tall. Write an inequality for height h.

42. A ride requires riders to be at least 60 inches tall. Write an inequality for height h.

43. A ride requires riders to be at least 61 inches tall. Write an inequality for height h.

44. A ride requires riders to be at least 62 inches tall. Write an inequality for height h.

45. A ride requires riders to be at least 63 inches tall. Write an inequality for height h.

12 of 22

Part D — Challenge

Questions 46–50

46. Challenge: Solve −2x > -10.

47. Challenge: Solve −2x > -12.

48. Challenge: Solve −2x > -14.

49. Challenge: Solve −2x > -16.

50. Challenge: Solve −2x > -18.

13 of 22

Answer Key — Questions 1–5

Answer + How to Solve

1. Answer: C

How to solve: A solution must be greater than 3; 4 works.

2. Answer: C

How to solve: A solution must be greater than 4; 5 works.

3. Answer: C

How to solve: A solution must be greater than 5; 6 works.

4. Answer: C

How to solve: A solution must be greater than 6; 7 works.

5. Answer: C

How to solve: A solution must be greater than 7; 8 works.

14 of 22

Answer Key — Questions 6–10

Answer + How to Solve

6. Answer: C

How to solve: A solution must be greater than 8; 9 works.

7. Answer: C

How to solve: A solution must be greater than 9; 10 works.

8. Answer: C

How to solve: A solution must be greater than 10; 11 works.

9. Answer: C

How to solve: A solution must be greater than 11; 12 works.

10. Answer: C

How to solve: A solution must be greater than 12; 13 works.

15 of 22

Answer Key — Questions 11–15

Answer + How to Solve

11. Answer: C

How to solve: A solution must be greater than 13; 14 works.

12. Answer: C

How to solve: A solution must be greater than 14; 15 works.

13. Answer: C

How to solve: A solution must be greater than 15; 16 works.

14. Answer: C

How to solve: A solution must be greater than 16; 17 works.

15. Answer: C

How to solve: A solution must be greater than 17; 18 works.

16 of 22

Answer Key — Questions 16–20

Answer + How to Solve

16. Answer: 2

How to solve: Subtract 1 from both sides.

17. Answer: 4

How to solve: Subtract 2 from both sides.

18. Answer: 6

How to solve: Subtract 3 from both sides.

19. Answer: 8

How to solve: Subtract 4 from both sides.

20. Answer: 10

How to solve: Subtract 5 from both sides.

17 of 22

Answer Key — Questions 21–25

Answer + How to Solve

21. Answer: 12

How to solve: Subtract 6 from both sides.

22. Answer: 14

How to solve: Subtract 7 from both sides.

23. Answer: 16

How to solve: Subtract 8 from both sides.

24. Answer: 18

How to solve: Subtract 9 from both sides.

25. Answer: 20

How to solve: Subtract 10 from both sides.

18 of 22

Answer Key — Questions 26–30

Answer + How to Solve

26. Answer: 22

How to solve: Subtract 11 from both sides.

27. Answer: 24

How to solve: Subtract 12 from both sides.

28. Answer: 26

How to solve: Subtract 13 from both sides.

29. Answer: 28

How to solve: Subtract 14 from both sides.

30. Answer: 30

How to solve: Subtract 15 from both sides.

19 of 22

Answer Key — Questions 31–35

Answer + How to Solve

31. Answer: h ≥ 49