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?

How can you tell when an equation has infinite solutions?

### Answer

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

1x + 9 = 1x + 8

2x + 9 = 2x + 8

3x + 9 = 3x + 8

etc.

x-2=x-3

2x + 3 = 2x + 4

5x+10=5x+9

2x+3=2x+4

2x+3=2x+4.

2x+9=2x+2

2x+5= 2x+4

1x+1=1x+2

3x+1=3x+2

4x+5=4x+4

5x+6=5x+5

x+7=x+8

2x+1+2x+3

3x+7=3x+6

4x+8=4x+7

2x+5= 2x+4

3x+1=3x+6

4x+5=4x+6

7x+3=7x-4

2x + 3 = 2x + 4

5x+8 = 5x+9

7x + 4 = 7x + 3

2x+4=2x+9

5x+1=5x+4

9x+4=9x+8

3x+1=3x=4

3x+3=3x+7

3x+5=3x+9

3x+9=3x+8

3x+9=3x+5

2x+1=2x+2

3x-5=3x+17

9x+3=9x+4

3x+7=3x+6

8x+5=8x+9

4x+5=4x+4

6x +7 = 6x + 2

9x+2= 9x+1

5x+3=5x-7

5x+3=5x+2

3x+2=3x+5

2x+1=2x+3

2x+7=2x+6

6x-5=6x+3

4x+5=4x+7

7x-2=7x+5

4x+8= 4x+2

486x+77=39x+45

7x-4=9x+7

2x+3=2x+8

5x+3=5x-6

4x+5=4x-6

1x+9=2x+4

3x+6=3x+7

3x+6=3x+7

8x+3=8x+5

2x+3=2x+4

x-3=x-2

2x + 3 = 2x + 8

4x-5=4x-6

2x+3=2×4

2x+4=2x+3

7x+3=2x+13

7x+3=2x=13

3x+7=3x+8

5x+7=5x+8

18x+4=18x+7

5x+7=5x+6

13x+9=13x+8

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

12x+5=12x+4

2x+4=2x+3

2x+4=2x+4

2x+4=2x+3

4x+5=4x+6

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

x+2=x+4

3x+ 6= 5x +4

-11x=4=-11x+-11

9x + 3 = 9x + 1

7x + 1 = 7x + 3