x is some integer
x+1 is the next consecutive integer
Consecutive integers are numbers like {5,6,7} or {11,12,13}. They are numbers that follow one after another.
We sum x and x+1 getting 26, which means,
x+(x+1) = 26
2x+1 = 26
2x = 26-1
2x = 25
x = 25/2
x = 12.5
But we run into a problem here. We made x an integer, but 12.5 is not an integer. So there are no integer solutions to the first equation
So there are no consecutive integers that add to 26.
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If your teacher said "consecutive even integers", then the equation would be
x+(x+2) = 26
2x+2 = 26
2x = 26-2
2x = 24
x = 24/2
x = 12
And we can see that x = 12 and x+2 = 12+2 = 14 add to 12+14 = 26
But again this only applies if your teacher wrote "consecutive even integers". With that "even" left out, there are no solutions.