Atriangle has sides measuring 5 inches and 8 inches. if x represents the length in inches of the third side, which inequality gives the range of possible values for x? .

Let x = third side
Using the Triangle Inequality theorem which states that the sum of two sides of a triangle must be longer than the third side and the difference of the two sides is the lower limit of the third side, the answer to your question is that the third side must be between 3 and 13, or written using inequalities, 3 < third side (or x) < 13 is the range.

Hello,
As I said in last message, it exist an triangular inequality that is seen in Europe! An pupil of 16 years old should know it!!!
If a,b,c are the sides of a triangle  it MUST exist these equality:
each side must be less then the sum of the others sides.

1)a<b+c
2)b<a+c
3)c<a+c

In the way:
5<8+x ==> x>-3 already done
8<x+5 ==>x>3
x<5+8==>x<13
thus 3<x<13

Did you enjoy all these words Melek, whose are written for nothing.
It is only bla-bla in english having nothing to do with a mathematic demonstration.