First...
[tex]Simplify\;-5x-6x \ \textgreater \ \mathrm{Add\:similar\:elements:}\:-5x-6x=-11x[/tex]
[tex]Simplify\;8-8n-n \ \textgreater \ \mathrm{Add\:similar\:elements:}\:-8n-n=-9n [/tex]
[tex]8 - 9n[/tex]
[tex]-11x\ \textless \ 8-9n[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)} \ \textgreater \ 11x\ \textgreater \ -8+9n[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}11 \ \textgreater \ \frac{11x}{11}\ \textgreater \ -\frac{8}{11}+\frac{9n}{11}[/tex]
[tex]Simplify \ \textgreater \ x\ \textgreater \ \frac{-8+9n}{11}[/tex]
Hope this helps!