The lengths of two sides of a triangle are 6 inches and 15 inches. if x is the length, in inches of the third side of this triangle, what inequality would represent values of x?

X is a positive length and thus x>0. By the triangle inequality we can say that x<6+15.

And thus the desired inequality is 0

The third side can't be shorter than 9 inches, otherwise it couldn't reach

between the ends of the 6 and the 15.

Also, it can't be longer than 21 inches, otherwise the 6 and the 15 couldn't

reach between the ends of the third side.

So 9 < x < 21