The sides of a triangle are 7, 4, n. If n is an integer, state the largest and smallest possible values of n.

The sides have to satisfy the triangle inequality, namely

The sum of the two shorter sides of a triangle must exceed the length of the third side.

The greatest value of n is less than 7+4=11, or n<11./

The smallest value of n is given by n+4>7, or n>3.

So putting the two statements together, we have

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