The triangle inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure on the third side.
Given the triangle above, that would mean
a + b > c
b + c > a
c + a > b
In the given problem, we have three sides with length 14, 17, and x. Using the triangle inequality theorem we can infer that
[tex]\begin{gathered} 14+17>x \\ 31>x \\ \text{or} \\ x<14+17 \\ x<31 \end{gathered}[/tex]
