Question 774828
Step 1.  Let {{{n}}} be the first integer.


Step 2.  Let {{{n+1}}} be the next consecutive integer


Step 3.  Then {{{n+n+1=35}}} since the their sum is {{{35}}}.


Step 4.  Solving the equation in Step 3 yields the following steps


{{{2n+1=35}}}


Subtract 1 from both sides of the equation


{{{2n+1-1=35-1}}}


{{{2n=34}}}


Divide by 2 to both sides of the equation


{{{2n/2=34/2}}}


{{{n=17}}} and {{{n+1=18}}} and note their sum is {{{35}}} as a check.


 ANSWER:  The two consecutive integers are {{{17}}} and {{{18}}}.