Question

triangle has sides measuring 2 inches and 7 inches If x represents the length in inches of the third side which inequality gives the range of possible values for x?

Answer 1

We know that
The sum of the lengths of any two sides of a triangle is greater than the length of the third side (Triangle Inequality Theorem)
so
inequality 1
$(2+7) \ \textgreater \ x \\ 9 \ \textgreater \ x \\ x \ \textless \ 9 in$

inequality 2
$(x+2) \ \textgreater \ 7 \\ x \ \textgreater \ 7-2 \\ x \ \textgreater \ 5 in$

the answer is
$5 in \ \textless \ x \ \textless \ 9 in$