 # Solving Equations with Variables on Both Sides

Directions: Using the digits 1 to 9, at most TWO times each, fill in the boxes to make an equation with no solutions. ### Hint

How can you tell when an equation has no solution?
How can you tell when an equation has infinite solutions?

There are many answers, but the coefficient of both x terms have to be the same and the constants must have different values. So, 2x + 3 = 2x + 4 is an answer because it is equivalent to 3 = 4, for which there is no solution.

Source: Robert Kaplinsky

## Difference of Squares and Sum of Cubes

Directions: Using the digits 0 to 9 at most one time each, place a digit …

1. 1x + 9 = 1x + 8
2x + 9 = 2x + 8
3x + 9 = 3x + 8
etc.

• 5x + 7= 5x + 8

2. 3. 2x + 3 = 2x + 4

4. 5x+10=5x+9

5. 2x+3=2x+4

6. 2x+3=2x+4.

7. 2x+9=2x+2

8. 9. 1x+1=1x+2

10. 11. 4x+5=4x+4

12. sophia antogiovanni

5x+6=5x+5

13. Preston Shanosky

x+7=x+8

14. 15. 3x+7=3x+6

16. 4x+8=4x+7

17. 2x+5= 2x+4

18. 3x+1=3x+6

19. 4x+5=4x+6

20. 7x+3=7x-4

21. 2x + 3 = 2x + 4

22. 23. 7x + 4 = 7x + 3

24. 2x+4=2x+9

25. 5x+1=5x+4

26. 9x+4=9x+8

27. 3x+1=3x=4

28. 29. • 3x+9=3x+8

30. 3x+9=3x+5

31. 2x+1=2x+2

32. 3x-5=3x+17

33. william hockstein

9x+3=9x+4

34. 3x+7=3x+6

35. 8x+5=8x+9

36. 4x+5=4x+4

37. 6x +7 = 6x + 2

38. 9x+2= 9x+1

39. 5x+3=5x-7

40. 5x+3=5x+2

41. 3x+2=3x+5

42. 2x+1=2x+3

43. 2x+7=2x+6

44. 6x-5=6x+3

45. 4x+5=4x+7

46. 7x-2=7x+5

47. 4x+8= 4x+2

48. 486x+77=39x+45

49. 50. 51. 5x+3=5x-6

52. 4x+5=4x-6

53. 1x+9=2x+4

54. 55. 56. 8x+3=8x+5

57. 58. x-3=x-2

59. 2x + 3 = 2x + 8

60. 4x-5=4x-6

61. 2x+3=2×4

62. 63. percydous Guerra

7x+3=2x+13

64. percydous Guerra

7x+3=2x=13

65. 3x+7=3x+8

66. 5x+7=5x+8

67. 18x+4=18x+7

68. 5x+7=5x+6

69. 13x+9=13x+8

70. Solving Equations with Variables on Both Sides
Directions: Using the digits 1 to 9, at most TWO times each, fill in the boxes to make an equation with no solutions.
_x +_ =_ x + _ -> original problem
2x +5 = 2x +9 -> my attempt

71. 72. 2x+4=2x+3

73. 2x+4=2x+4

74. 2x+4=2x+3

75. 4x+5=4x+6

76. To keep in line with the structure of other open middle problems, perhaps you could change it to

Directions: Using the digits 1 to 9, at most ONE time each, fill in the boxes to make an equation with no solutions.

__ x + ___ = ___ ( ___ x + ___ )

or

__ x + ___ = ___ x + ___ – ___ x

• Amy, nice job. I used your suggestion and rewrote it. Yours is a huge improvement on the problem.

77. 78. 3x+ 6= 5x +4

79. -11x=4=-11x+-11

80. 81. 82. 