Answer :
[tex]q+3\geq9 \vee 9q+5<14\\
q\geq 6 \vee 9q<9\\
q\geq 6 \vee q<1\\
q\in(-\infty,1) \cup \langle6,\infty)[/tex]
[tex]First\ calculate\ inequalities\\\\
q+3 \geq 9\ \ \ |subtract\ 3\\
q \geq 6\\\\
or\\\\9q+5<14\ \ \ | subtract \ 5\\
9q <9\ \ \ |divide\ by\ 9\\q<1\\\\Now\ find\ sum\ of\ those\ results\\\\
q \geq 6\ \ or \ \ q<1\\\\
Sum\ is\ :\\
q\in(-\infty,1) \cup [6,+\infty) [/tex]