Answer:
[tex]\mathrm{D.\:}14<x<32[/tex]
Step-by-step explanation:
In any triangle, the sum of any two sides must be greater than the other side. Therefore, in the given triangle with side lengths [tex]9[/tex] and [tex]12[/tex], we can write the following inequalities:
[tex]\begin{cases}(x-2)+9>21,\\21+9>(x-2)\\\end{cases}[/tex]
Solving these inequalities, we get:
[tex]x-2>12,\\x>14\\\\30>x-2,\\x<32[/tex].
Combining this into one inequality gives us:
[tex]\mathrm{D.\:}14<x<32[/tex].
