Question 933235
by definition: Integers are like whole numbers, but they also include negative numbers, but still no fractions allowed!

 let the first integer be {{{x+1}}}, the second is {{{x+2}}} and the third is {{{x+3}}}

the smallest integer is {{{x+1}}}

if the sum of three consecutive integers is {{{26}}} more than the smallest integer, then we have:

{{{(x+1)+(x+2)+(x+3)=x+26}}}...solve for {{{x}}}

{{{x+1+x+2+x+3=x+26}}}

{{{3x+3=x+26}}}

{{{3x-x=26-3}}}

{{{2x=23}}}

{{{x=23/2}}} it is not an integer which is a number with {{{no}}} fractional part 

let’s try with

three consecutive even integers ---> {{{x}}} ,{{{(x + 2)}}}, and {{{ (x + 4) }}}

{{{x + (x + 2) + (x + 4)=x+26}}}
{{{x + x + 2 + x + 4=x+26}}}
{{{3x + 6=x+26}}}
{{{3x -x=26-6}}}
{{{2x=20}}}
{{{x=10}}}

your integers are: {{{highlight(10)}}},{{{highlight(12)}}}, and {{{highlight(14)}}}

try also three consecutive odd integers are of the form:

{{{(2x+1)+ (2x+3)+ (2x+5)=(2x+1)+26}}}

{{{2x+1+ 2x+3+ 2x+5=2x+1+26}}}

{{{6x+9=2x+27}}}

{{{6x-2x=27-9}}}

{{{4x=18}}}

{{{x=18/4}}}

{{{x=9/2}}}....it is {{{not}}} an integer either

so, you must have three consecutive {{{even}}} integers to have a solution