If three times the smaller of two consecutive integers is added to four times the larger, the result is 102. find the smallest interger

Two consecutive integers are n and n+1 and of course n+1>n.

3n+4 (n+1) = 102 perform indicated multiplication on left side

3n+4n+4=102 combine like terms on left side 3n+4n=7n

7n+4=102 subtract 4 from both sides

7n=98 divide both sides by 7

n=14

So the smaller integer is 14.