bearing in mind that an absolute value expression is in effect a piece-wise expression, since it has a positive and a negative sibling.
[tex] \bf 9|x+1|-6<-42\implies 9|x+1|<-36\implies |x+1|<\cfrac{-36}{9}
\\\\\\
|x+1|<-4\implies
\begin{cases}
+(x+1)<-4\implies \boxed{x<-5}\\\\[-0.5em]
\hrulefill\\\\
-(x+2)<-4\implies x+2>4\\
\boxed{x>2}
\end{cases} [/tex]
