1 of 22

UST Middle School Algebra I Challenge

Week 2 — Linear Equations

Focus: Multi-step equations, variables on both sides

2 of 22

Weekly Format

Week 2

Part A — 15 Multiple Choice

Part B — 15 Fill in the Blank

Part C — 15 Word / Open-Response Problems

Part D — 5 Challenge Problems

Answer key and step-by-step explanations follow the questions.

3 of 22

Part A — Multiple Choice

Questions 1–5

1. Solve 4x − 7 = 5. A) 3 B) 10 C) 12 D) 2

2. Solve 4x − 7 = 9. A) 4 B) 11 C) 16 D) 3

3. Solve 4x − 7 = 13. A) 5 B) 12 C) 20 D) 4

4. Solve 4x − 7 = 17. A) 6 B) 13 C) 24 D) 5

5. Solve 4x − 7 = 21. A) 7 B) 14 C) 28 D) 6

4 of 22

Part A — Multiple Choice

Questions 6–10

6. Solve 4x − 7 = 25. A) 8 B) 15 C) 32 D) 7

7. Solve 4x − 7 = 29. A) 9 B) 16 C) 36 D) 8

8. Solve 4x − 7 = 33. A) 10 B) 17 C) 40 D) 9

9. Solve 4x − 7 = 37. A) 11 B) 18 C) 44 D) 10

10. Solve 4x − 7 = 41. A) 12 B) 19 C) 48 D) 11

5 of 22

Part A — Multiple Choice

Questions 11–15

11. Solve 4x − 7 = 45. A) 13 B) 20 C) 52 D) 12

12. Solve 4x − 7 = 49. A) 14 B) 21 C) 56 D) 13

13. Solve 4x − 7 = 53. A) 15 B) 22 C) 60 D) 14

14. Solve 4x − 7 = 57. A) 16 B) 23 C) 64 D) 15

15. Solve 4x − 7 = 61. A) 17 B) 24 C) 68 D) 16

6 of 22

Part B — Fill in the Blank

Questions 16–20

16. Solve 3x + 6 = 21. x = ___.

17. Solve 3x + 6 = 24. x = ___.

18. Solve 3x + 6 = 27. x = ___.

19. Solve 3x + 6 = 30. x = ___.

20. Solve 3x + 6 = 33. x = ___.

7 of 22

Part B — Fill in the Blank

Questions 21–25

21. Solve 3x + 6 = 36. x = ___.

22. Solve 3x + 6 = 39. x = ___.

23. Solve 3x + 6 = 42. x = ___.

24. Solve 3x + 6 = 45. x = ___.

25. Solve 3x + 6 = 48. x = ___.

8 of 22

Part B — Fill in the Blank

Questions 26–30

26. Solve 3x + 6 = 51. x = ___.

27. Solve 3x + 6 = 54. x = ___.

28. Solve 3x + 6 = 57. x = ___.

29. Solve 3x + 6 = 60. x = ___.

30. Solve 3x + 6 = 63. x = ___.

9 of 22

Part C — Word / Open Response

Questions 31–35

31. Five tickets plus a $12 fee cost $72. Find one ticket price.

32. Five tickets plus a $12 fee cost $77. Find one ticket price.

33. Five tickets plus a $12 fee cost $82. Find one ticket price.

34. Five tickets plus a $12 fee cost $87. Find one ticket price.

35. Five tickets plus a $12 fee cost $92. Find one ticket price.

10 of 22

Part C — Word / Open Response

Questions 36–40

36. Five tickets plus a $12 fee cost $97. Find one ticket price.

37. Five tickets plus a $12 fee cost $102. Find one ticket price.

38. Five tickets plus a $12 fee cost $107. Find one ticket price.

39. Five tickets plus a $12 fee cost $112. Find one ticket price.

40. Five tickets plus a $12 fee cost $117. Find one ticket price.

11 of 22

Part C — Word / Open Response

Questions 41–45

41. Five tickets plus a $12 fee cost $122. Find one ticket price.

42. Five tickets plus a $12 fee cost $127. Find one ticket price.

43. Five tickets plus a $12 fee cost $132. Find one ticket price.

44. Five tickets plus a $12 fee cost $137. Find one ticket price.

45. Five tickets plus a $12 fee cost $142. Find one ticket price.

12 of 22

Part D — Challenge

Questions 46–50

46. Challenge: Solve 2(x+3)+x=24.

47. Challenge: Solve 2(x+3)+x=27.

48. Challenge: Solve 2(x+3)+x=30.

49. Challenge: Solve 2(x+3)+x=33.

50. Challenge: Solve 2(x+3)+x=36.

13 of 22

Answer Key — Questions 1–5

Answer + How to Solve

1. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=3.

2. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=4.

3. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=5.

4. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=6.

5. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=7.

14 of 22

Answer Key — Questions 6–10

Answer + How to Solve

6. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=8.

7. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=9.

8. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=10.

9. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=11.

10. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=12.

15 of 22

Answer Key — Questions 11–15

Answer + How to Solve

11. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=13.

12. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=14.

13. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=15.

14. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=16.

15. Answer: A

How to solve: Add 7 to both sides, then divide by 4: x=17.

16 of 22

Answer Key — Questions 16–20

Answer + How to Solve

16. Answer: 5