Answer:
[tex]6<x<8.[/tex]
Step-by-step explanation:
The sides MN, NP and MP of the triangle MNP should satisfy inequalities:
- [tex]MN+NP>MP;[/tex]
- [tex]MN+MP>NP;[/tex]
- [tex]NP+MP>MN.[/tex]
Then
[tex]\left\{\begin{array}{l}4x+9+x+5>7x-20\\4x+9+7x-20>x+5\\x+5+7x-20>4x+9\end{array}\right..[/tex]
Simplify this system:
[tex]\left\{\begin{array}{l}4x+x-7x>-9-5-20\\4x+7x-x>20-9+5\\x+7x-4x>20-5+9\end{array}\right.\Rightarrow \left\{\begin{array}{l}-2x>-16\\10x>16\\4x>24\end{array}\right.\Rightarrow \left\{\begin{array}{l}x<8\\x>1.6\\x>6\end{array}\right..[/tex]
Thus, the range of possible values for x is [tex]6<x<8.[/tex]
