Question 1013958

 let the smaller one be represented by {{{x}}} and the next integer up from it is {{{x + 1}}}

if the sum of two consecutive integers is at most {{{3}}}, we have

{{{x+x + 1<=3}}}

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

{{{2x <=3-1}}}

{{{2x <=2}}}

{{{x <=2/2}}}

{{{x <=1}}}->the smaller integer

{{{x +1<=2}}}->the greater integer

 so, the greatest possible value for the greater integer is {{{x=2}}}