Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to write three equations whose solution is -1/2.

### Hint

What does it mean to be a solution of the equation?

How would you check if a value is a solution to an equation?

What kind of numbers would you put in for the coefficients of x?

How would you check if a value is a solution to an equation?

What kind of numbers would you put in for the coefficients of x?

### Answer

There are many arrangements. Here is one set.

2x + 5 = 4x + 6

2x + 7 = 4x + 8

8x + 5 = 4x + 3

2x + 5 = 4x + 6

2x + 7 = 4x + 8

8x + 5 = 4x + 3

Source: Daniel Luevanos

2x + 5 = 4x + 6

2x + 7 = 4x + 8

8x + 5 = 4x + 3

x+4=3x+5

x+6=3x+7

2x+5=4x+6

2x+3=4x+4

4x+2=8x+4

2x+1+4x+2

5x+7=3x+6

3x+10=x+9

6x+14=4x+13

-3x+1=-x+2

2x+1=4x+2

6x+3=8x+4

8x+3=4x+1

5x+7=3x+6

8x+3=4x+1

4x+2=8x+4

2x+4=4x+5

2x+3=4x+4

4x+5=8x+6

2x+3=4x+4

6x-4=-2+6x

2x+4= 4x+5

4x+6=6x+7

6x+7=8x+8

8x+8+10x+9

2x + 6 = 4x + 7

2x + 7 = 4x + 8

8x + 5 = 4x + 3

7x+8=5x+7

x+6=3x+7

4x+1=2x+5

5x+7=7x+8

4x+6=6x+7

3x+5=5x+6

3x+1=6x+2

*4x+1=6x+2

7x+8=5x+7

x+6+3x+7

* 4x+6=6x+7

7x+8=5x+7

x+6+3x+7

4x+6=6x+7

2x + 5 = 4x + 6

2x + 7 = 4x + 8

8x + 5 + 4x + 3

x+9 = 3x+10

4x+9 = 2x+8

6x + 10 = 4x +9

6x+3=4x+2

x+8.5=2x+9

2x+7=-8x+2

3x+3=x+2

4x+4=2x+3

5x+5=3x+4

3x+5=x+4

4x+6=2x+5

5x+7=3x+6

4x+6=8x+8

8x+9=4x+7

2x+5=4x+6

2x+5=4x+6

3x+1=6x+5

2x+4=4x+5

5x+7=3x+6

6x+7=8x+8

4x+2=8x+4

6x+6=2x+4

3x+1=5x+2

5x+4=3x+3

6x+3=4x+2

3x+1=6x+5

8x+5+4x+3

6x+3=4x+2

3x+1=6x+5

8x+6+4x+4

2x+1=4x+0

6x+2=8x+1

3x+1=x+2

8x-1=10x

4x-1=2x-2

12x-1=16x+1

6x-4=4x-5

8x+9=4x+7

12x-6=10x-7

-6-x=-5+x

x=-8(2)/32

8+x=20+x-12

2x+3=4x+4

4x+2=8x+4

2x+1=4x+2

x+3 = 2x+5

6x+ 1= 3x+ 2

1.5x+ 2= 3x+4

3x + 1 = 2x + 1/2

Answer: x = -1/2

4x+6=3-2x

1041x+500=41x

5x/2+27x/2=-9x/2+10

6x + 2 = 10x + 4

10x + 3 = 16x + 6

2x + 3 = 4x + 4

8x+7=4x+5

8x+2=6x+1

6x+7=2x+5

4x+3=2x+2

8x+9=6x+8

3x+2=x+1

6x+5=8x+6

10x+10=12x+11

36x+8=38x+9

3x+5=5x=6

4x+5=3x+3

8x+8=7x+6

4x+2=8x+4

3x+5=5x=6

8x+2=6x+1

x + 2 = 3x +3

-11x – 6 = 3x +1

5x +8 = 3x + 7

just realized 2nd one had an 11

changed it to – 9x – 6 = 5x +1

-7x-5=9x+3

6x+8=4x+7

-3x-6=7x-1

2x+3=6x+5

8x+4=6x+3

6x+9=4x+8

2x+3=4x+4

-2x-2=-4x-3

3x+12=x+11

2x+5=4x+6.

4x+4=2x+3.

3x+1=6x+2

Create an Equation with a Given Solution

Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to write three equations whose solution is -1/2

_x + _ =_x + _ -> original problem

6x +9 =4x +8 -> my attempt

4x + 7 = 6x + 8 —> -1 = 2x —> -0.5 = x

2x + 3 = 6x + 5 —> -2 = 4x —> -0.5 = x

4x + 5 = 8x + 7 —> -2 = 4x —> -0.5 = x

3x + 6 = 5x + 7

3x + 8 = 5x + 9

9x + 6 = 5x + 4

4x + 7 = 6x + 8

3x + 8 = 5x + 9

9x + 6 = 5x + 4