Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create two expressions that are equivalent to one another.
Hint
What values will make the constants equivalent? What values will make the variable terms equivalent?
Answer
Here are some possibilities:
1x + 2x + 9 + 3x = 4 + 6x + 5;
1x + 2x + 8 + 4x = 3 + 7x + 5
1x + 2x + 9 + 3x = 4 + 6x + 5;
1x + 2x + 8 + 4x = 3 + 7x + 5
Source: Will Case
answer 3x+2x+8+4x=1+9x+7
8x+5x+2+4x=4+5x+9
good
Answer: 1x+2x+3+1x=4x+3
you cant re-use a number
5x + 3x + 4 + 1x = 3 + 9x + 1
I changed my answer. 4x + 2x + 8 + 3x = 7 + 9x + 1
3x + 8x + 4+ x = 2 + 12x + 2
3x+1X+8+5x=6+9x+2
answer 5x +3x + 4 + 2x = 3 + 7 + 4x
Here are all the solutions (excluding swapping addends):
1x + 2x + 7 + 5x = 3 + 8x + 4
1x + 2x + 7 + 6x = 3 + 9x + 4
1x + 2x + 8 + 4x = 3 + 7x + 5
1x + 2x + 8 + 6x = 3 + 9x + 5
1x + 2x + 9 + 3x = 4 + 6x + 5
1x + 2x + 9 + 4x = 3 + 7x + 6
1x + 2x + 9 + 5x = 3 + 8x + 6
1x + 3x + 6 + 5x = 2 + 9x + 4
1x + 3x + 7 + 4x = 2 + 8x + 5
1x + 3x + 8 + 5x = 2 + 9x + 6
1x + 3x + 9 + 4x = 2 + 8x + 7
2x + 3x + 6 + 4x = 1 + 9x + 5
2x + 3x + 7 + 4x = 1 + 9x + 6
2x + 3x + 8 + 4x = 1 + 9x + 7
2X+4X+1+3X=2+5X+3