The sum of any two sides of a triangle is strictly greater than the third side.

x + 3 > 7, 3 + 7 > x, x + 7 > 3

The third one is obviously true, so we need only look at the first two

x + 3 > 7, 3 + 7 > x 
    x > 4     10 > x

So 4 < x < 10

So the third side must be between 4 and 10 inches, exclusive of both.

Edwin