Question 937012

given:

{{{2<x< 7}}}

Now, a triangle {{{must}}} be such that the {{{sum}}} of {{{any}}}{{{ two}}} sides {{{must}}} be {{{greater}}} than the {{{third}}} side.

So, immediately, we are down to {{{3}}}, {{{4}}}, {{{5}}}, {{{6}}} under given conditions.

If {{{x = 3}}} then {{{2+3 < 7}}} --- not a triangle!
if {{{x = 4}}} then {{{2 + 4 < 7}}} -- not a triangle
if {{{x = 5}}} then {{{2 + 5 = 7}}} -- not a triangle
if x = 6 then {{{2+ 6 > 7}}} -- {{{triangle}}}
so, {{{1}}} value of {{{x}}} works; so, answer is {{{one}}}