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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.

Hint

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?

Answer

Answer

There are many arrangements. Here is one set.
2x + 5 = 4x + 6
2x + 7 = 4x + 8
8x + 5 = 4x + 3

Source: Daniel Luevanos

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52 comments

  1. 2x + 5 = 4x + 6
    2x + 7 = 4x + 8
    8x + 5 = 4x + 3

  2. x+4=3x+5

    x+6=3x+7

    2x+5=4x+6

  3. 2x+3=4x+4

    4x+2=8x+4

    2x+1+4x+2

  4. 5x+7=3x+6
    3x+10=x+9
    6x+14=4x+13

  5. 2x+1=4x+2
    6x+3=8x+4
    8x+3=4x+1

  6. 5x+7=3x+6
    8x+3=4x+1
    4x+2=8x+4

  7. sophia antogiovanni

    2x+4=4x+5
    2x+3=4x+4
    4x+5=8x+6

  8. 2x+3=4x+4

  9. 2x+4= 4x+5

  10. 4x+6=6x+7
    6x+7=8x+8
    8x+8+10x+9

  11. 2x + 6 = 4x + 7
    2x + 7 = 4x + 8
    8x + 5 = 4x + 3

  12. 7x+8=5x+7
    x+6=3x+7
    4x+1=2x+5

  13. 5x+7=7x+8
    4x+6=6x+7
    3x+5=5x+6

  14. 3x+1=6x+2

  15. 7x+8=5x+7
    x+6+3x+7
    * 4x+6=6x+7

  16. 7x+8=5x+7
    x+6+3x+7
    4x+6=6x+7

  17. 2x + 5 = 4x + 6
    2x + 7 = 4x + 8
    8x + 5 + 4x + 3

  18. x+9 = 3x+10
    4x+9 = 2x+8
    6x + 10 = 4x +9

  19. 6x+3=4x+2
    x+8.5=2x+9
    2x+7=-8x+2

  20. 3x+3=x+2
    4x+4=2x+3
    5x+5=3x+4

  21. 4x+6=8x+8
    8x+9=4x+7
    2x+5=4x+6

  22. 2x+5=4x+6
    3x+1=6x+5
    2x+4=4x+5

  23. 5x+7=3x+6
    6x+7=8x+8
    4x+2=8x+4

  24. 6x+3=4x+2
    3x+1=6x+5
    8x+5+4x+3

  25. 6x+3=4x+2
    3x+1=6x+5
    8x+6+4x+4

  26. 2x+1=4x+0
    6x+2=8x+1
    3x+1=x+2

  27. 8x-1=10x
    4x-1=2x-2
    12x-1=16x+1

  28. 6x-4=4x-5
    8x+9=4x+7
    12x-6=10x-7

  29. william hockstein

    -6-x=-5+x
    x=-8(2)/32
    8+x=20+x-12

  30. 2x+3=4x+4
    4x+2=8x+4
    2x+1=4x+2

  31. x+3 = 2x+5

  32. 4x+6=3-2x
    1041x+500=41x
    5x/2+27x/2=-9x/2+10

  33. 6x + 2 = 10x + 4
    10x + 3 = 16x + 6
    2x + 3 = 4x + 4

  34. 8x+7=4x+5
    8x+2=6x+1
    6x+7=2x+5

  35. 4x+3=2x+2
    8x+9=6x+8
    3x+2=x+1

  36. 6x+5=8x+6
    10x+10=12x+11
    36x+8=38x+9

  37. 3x+5=5x=6
    4x+5=3x+3
    8x+8=7x+6

  38. 4x+2=8x+4
    3x+5=5x=6
    8x+2=6x+1

  39. x + 2 = 3x +3
    -11x – 6 = 3x +1
    5x +8 = 3x + 7

  40. -7x-5=9x+3
    6x+8=4x+7
    -3x-6=7x-1

  41. 2x+3=6x+5
    8x+4=6x+3
    6x+9=4x+8

  42. 2x+3=4x+4
    -2x-2=-4x-3
    3x+12=x+11

  43. 2x+5=4x+6.
    4x+4=2x+3.
    3x+1=6x+2

  44. 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

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