# 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

## Multiplying Monomials

Directions: Using the digits 0 to 9 at most one time each to create a …

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

2. 2x + 3 = 2x + 4

3. 5x+10=5x+9

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

5. 2x+9=2x+2

6. 1x+1=1x+2

7. sophia antogiovanni

5x+6=5x+5

8. Preston Shanosky

x+7=x+8

9. 4x+8=4x+7

10. 2x+5= 2x+4

11. 7x+3=7x-4

12. 2x + 3 = 2x + 4

13. 7x + 4 = 7x + 3

14. 2x+4=2x+9

15. 5x+1=5x+4

16. 3x+1=3x=4

17. 2x+1=2x+2

18. 3x-5=3x+17

19. william hockstein

9x+3=9x+4

20. 6x +7 = 6x + 2

21. 9x+2= 9x+1

22. 5x+3=5x+2

23. 2x+1=2x+3

24. 7x-2=7x+5

25. 4x+8= 4x+2

26. 486x+77=39x+45

27. 5x+3=5x-6

28. 2x + 3 = 2x + 8

29. 4x-5=4x-6

30. 2x+3=2×4

31. percydous Guerra

7x+3=2x+13

32. percydous Guerra

7x+3=2x=13

33. 3x+7=3x+8

34. 5x+7=5x+8

35. 5x+7=5x+6

36. 13x+9=13x+8

37. 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

38. 2x+4=2x+3

39. 4x+5=4x+6

40. 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

41. 3x+ 6= 5x +4

42. -11x=4=-11x+-11