Answer: The required compound inequality is ![3](https://tex.z-dn.net/?f=3%3Cn%3C15.)
Step-by-step explanation: We are given that the lengths of the sides of a sandbox are 9 ft, 6 ft and n ft.
We are to write a compound inequality that describes all possible lengths of n.
Since the sandbox has three sides, so it must be a triangle.
Also, we know that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
So, we have
![9+6>n\\\\\Rightarrow 15>n\\\\\Rightarrow n](https://tex.z-dn.net/?f=9%2B6%3En%5C%5C%5C%5C%5CRightarrow%2015%3En%5C%5C%5C%5C%5CRightarrow%20n%3C15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%28i%29)
![6+n>9\\\\\Rightarrow n>9-6\\\\\Rightarrow n>3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)](https://tex.z-dn.net/?f=6%2Bn%3E9%5C%5C%5C%5C%5CRightarrow%20n%3E9-6%5C%5C%5C%5C%5CRightarrow%20n%3E3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%28ii%29)
and
![9+n>6\\\\\Rightarrow n>6-9\\\\\Rightarrow n>-3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)](https://tex.z-dn.net/?f=9%2Bn%3E6%5C%5C%5C%5C%5CRightarrow%20n%3E6-9%5C%5C%5C%5C%5CRightarrow%20n%3E-3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%28iii%29)
Combining inequalities (i), (ii) and (iii), we get
![3](https://tex.z-dn.net/?f=3%3Cn%3C15.)
Thus, the required compound inequality is ![3](https://tex.z-dn.net/?f=3%3Cn%3C15.)