Answer :
[tex]9|x+8|+10 <55\\
9|x+8|<45\\
|x+8|<5\\
x+8<5 \wedge x+8>-5\\
x<-3 \wedge x>-13\\
x\in(-13,-3)[/tex]
[tex] 9|x+8|+10 <55\ \ |\ subtract\ 10\ to\ both\ sides\\\\ 9|x+8|<45\ \ | \ divide \ each \ term \ by \ 9\\\\|x+8|<5\\\\ x+8<5\ \ \ \wedge \ \ \ x+8>-5\ \ |\ subtract\ 8 \ to\ both\ sides \\\\x<-3 \ \ \ \wedge \ \ \ x>-13 \\\\ x\in(-13,-3) [/tex]