Let's say we have a triangle with three side lengths.
This triangle is really flat. So much so that you could put it on a number line.
It literally cannot get any flatter, and the largest side literally cannot get any bigger.
Well, the smaller two sides would add up to equal the third.
From this we have realized something: The largest side of any triangle cannot be larger than the sum of the other two.
Let's think back to our problem.
What are the possibilities for [tex]x[/tex]?
If [tex]x[/tex] was the biggest side, it couldn't be any bigger than 40.
If [tex]x[/tex] was a smaller side, then that would make 25 the bigger side.
15 and [tex]x[/tex] together can't be any bigger than 25, so [tex]x[/tex] has to be less than 10.
Since it's a scalene triangle, x cannot be 15 or 25 either, so add that too.
[tex]\{x|10\ \textless \ x\ \textless \ 40,\ x\neq15, x\neq25\}[/tex]
