Only Geniuses Can Solve All 50: Hard SAT Linear Equations Challenge!

🧮 50 Hard SAT Linear Equation Questions (MCQs)

🔹 Questions

1–10

1. 3(2x − 5) + 4 = 2(x + 7)
   A) 3 B) 4 C) 5 D) 6

2. 5(x − 2) = 3(x + 4) + 2
   A) 6 B) 7 C) 8 D) 9

3. 4x − 3(2x − 1) = 7
   A) -2 B) -3 C) 2 D) 3

4. 2(x + 5) − 3(x − 2) = 4
   A) 8 B) 9 C) 10 D) 11

5. (x/2) + (x/3) = 10
   A) 10 B) 12 C) 15 D) 20

6. 6(x − 1) = 2(2x + 5)
   A) 4 B) 5 C) 6 D) 7

7. 3x + 7 = 2(x + 9)
   A) 9 B) 10 C) 11 D) 12

8. 8x − 4 = 2(3x + 6)
   A) 6 B) 7 C) 8 D) 9

9. 5(x + 1) − 3(x − 2) = 20
   A) 5 B) 6 C) 7 D) 8

10. 7x − 2(3x − 4) = 10
    A) 2 B) 3 C) 4 D) 5

11–20

11. (x − 3)/2 = (x + 5)/4
    A) 11 B) 12 C) 13 D) 14

12. (2x + 1)/3 = (x − 2)/2
    A) -8 B) -7 C) -6 D) -5

13. (x/4) + 5 = (x/2) − 3
    A) 32 B) 28 C) 24 D) 20

14. (3x − 2)/5 = (x + 6)/3
    A) 12 B) 13 C) 14 D) 15

15. (x − 1)/3 + (x − 2)/3 = 6
    A) 9 B) 10 C) 11 D) 12

16. (2x + 5)/4 = (x − 1)/2
    A) 7 B) 8 C) 9 D) 10

17. (3x − 1)/2 = x + 4
    A) 8 B) 9 C) 10 D) 11

18. (x + 2)/3 = (x − 4)/2
    A) 14 B) 16 C) 18 D) 20

19. (5x − 3)/2 = (x + 7)
    A) 5 B) 6 C) 7 D) 8

20. (x − 6)/2 + (x − 2)/4 = 5
    A) 6 B) 7 C) 8 D) 9

21–30 (Word Problems)

21. Twice a number plus 7 equals three times the number minus 5.
    A) 12 B) 10 C) 8 D) 6

22. A number decreased by 4 equals half the number plus 6.
    A) 20 B) 18 C) 16 D) 14

23. Three consecutive integers sum to 36. What is the smallest?
    A) 10 B) 11 C) 12 D) 13

24. The sum of a number and its double is 45.
    A) 10 B) 12 C) 15 D) 18

25. A number is 5 more than twice another number. If their sum is 29, find the larger number.
    A) 18 B) 19 C) 20 D) 21

26. The perimeter of a rectangle is 50. Length is 5 more than width. Find width.
    A) 10 B) 11 C) 12 D) 13

27. A number plus its half equals 18.
    A) 10 B) 11 C) 12 D) 13

28. The sum of two numbers is 40. One is 8 more than the other. Find smaller number.
    A) 14 B) 15 C) 16 D) 17

29. A number multiplied by 3 minus 6 equals 24.
    A) 8 B) 9 C) 10 D) 11

30. A number divided by 4 plus 2 equals 6.
    A) 12 B) 14 C) 16 D) 18

31–40 (Concept-Based)

31. x − 5 = x + 3
    A) 8 B) No solution C) Infinite D) 2

32. 2(x + 3) = 2x + 6
    A) No solution B) Infinite C) 3 D) 6

33. 5(x − 2) = 5x − 10
    A) Infinite B) No solution C) 2 D) 5

34. 4x + 8 = 4(x + 2)
    A) Infinite B) No solution C) 2 D) 4

35. 3(x − 1) = 3x − 5
    A) Infinite B) No solution C) 4 D) 5

36. 7x + 2 = 7(x + 1)
    A) Infinite B) No solution C) 1 D) 2

37. 6(x − 1) = 6x − 6
    A) Infinite B) No solution C) 1 D) 6

38. 2x + 5 = 2x + 7
    A) No solution B) Infinite C) 2 D) 7

39. 9(x − 1) = 9x − 9
    A) Infinite B) No solution C) 1 D) 9

40. 4x + 1 = 4x + 2
    A) Infinite B) No solution C) 1 D) 2

41–50 (Challenging Mix)

41. 3(x − 2) + 2(x + 1) = 20
    A) 4 B) 5 C) 6 D) 7

42. 2(x + 4) + 3(x − 1) = 25
    A) 3 B) 4 C) 5 D) 6

43. 5(x − 3) + 2(x + 2) = 29
    A) 4 B) 5 C) 6 D) 7

44. 4(x + 2) − 3(x − 1) = 13
    A) 3 B) 4 C) 5 D) 6

45. 6(x − 1) + 2(x + 3) = 34
    A) 4 B) 5 C) 6 D) 7

46. 7(x + 2) − 3(x − 4) = 38
    A) 4 B) 5 C) 6 D) 7

47. 8(x − 1) + 2(x + 5) = 50
    A) 4 B) 5 C) 6 D) 7

48. 3(x + 4) + 4(x − 2) = 30
    A) 4 B) 5 C) 6 D) 7

49. 5(x − 1) + 5(x + 1) = 50
    A) 4 B) 5 C) 6 D) 7

50. 9(x − 2) + x = 40
    A) 4 B) 5 C) 6 D) 7

✅ Answer Key

1-D, 2-C, 3-B, 4-A, 5-B, 6-B, 7-C, 8-C, 9-C, 10-B
11-C, 12-B, 13-A, 14-D, 15-D, 16-B, 17-B, 18-B, 19-B, 20-C
21-A, 22-C, 23-B, 24-C, 25-B, 26-C, 27-C, 28-C, 29-A, 30-C
31-B, 32-B, 33-A, 34-A, 35-B, 36-B, 37-A, 38-A, 39-A, 40-B
41-B, 42-C, 43-B, 44-C, 45-C, 46-C, 47-B, 48-C, 49-B, 50-C