X is some integer
X+1 is the consecutive integer
Consecutive interferes are numbers like { 5,6,7 } or { 11,12,13 }. They are numbers that follow after one 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
We made x an internet but 12.5 isn’t a integer so there are no solutions to the first integer equation.
So there are no consecutive integers that add up to 26.
If your teacher said consecutive even integers then your equation would be
x+(x+2)=26
2x+2=26
2x=24
x=24/2
x=12
And we can see that x=12 and x+2=12+2=14 add 12+14=26
Thar only applies if your teacher wrote consecutive even integers. With that even left out there are no solutions