Hey!
Let's write the problem.
[tex]22q+73\ \textgreater \ 52q+63[/tex]
Subtract [tex]73[/tex] from both sides.
[tex]22q+73-73\ \textgreater \ 52q+63-73[/tex]
[tex]22q\ \textgreater \ 52q-10[/tex]
Subtract [tex]52q[/tex] from both sides.
[tex]22q-52q\ \textgreater \ 52q-10-52q[/tex]
[tex]-30q\ \textgreater \ -10[/tex]
Since we don't want negative, we will multiply both sides by [tex]-1[/tex].
[tex]\left(-30q\right)\left(-1\right)\ \textless \ \left(-10\right)\left(-1\right)[/tex]
[tex]30q\ \textless \ 10[/tex]
Divide both sides by [tex]30[/tex].
[tex]\frac{30q}{30}\ \textless \ \frac{10}{30}[/tex]
Our final answer would be,
[tex]q\ \textless \ \frac{1}{3}[/tex]
Thanks!
-TetraFish
