the sides of a triangle are 7, 4, n. if n is an integer, state the largest and smallest possible values of n.smallest value-largest value-plz

The smallest value it could be is 4 and the largest value it could be is 10.

The triangle inequality theorem states that any two sides of a triangle must have a sum greater than the third side.  Given the two sides we have, 7 and 4, the sum would be 11; this would mean that the missing side could be no more than 10.

If we take the unknown side and the smallest one we're given, we would have the inequality 
n+4>7

Subtracting 4 from both sides we would have n>3.  That means it would have to be the next integer up, which would be 4.