(1) According to the division rule of rational numbers, "When two numbers are divided, the sign is negative". have

1)3x- 19 < 0 2)3x- 19 > 0

2x-9>0 2x-9>0

Solve the inequality group 1) and get 9/2 < x < 19/3. Solve inequality 2) and there is no solution.

So the solution set of the original inequality is 9/2 < x < 19/3.

(2) 1) From (1) we know that the integer solutions of x are 5 and 6.

If the difference of any one of the three sides of a triangle is greater than the sum of the other two sides, the solution of 6-5 < c < 6+5 is1< c <1.

2)c=5 or 6

When c=5, the circumference of ABC triangle is 16.

When c = 6, the circumference of ABC triangle is 17.