Verified Answer :

\(\frac{v-9}{10v} +6=11\)

Subtracting 6 on both sides, we get,

\(\frac{v-9}{10v} =11-6\)

\(\frac{v-9}{10v} =5\)

Multiplying by 10v on both sides , we get,

\(\frac{v-9}{10v}*10v =5 *10v\)

\(v-9=50v\)

\(-9 = 50v -v\)

\(-9=49v\)

\(\frac{-9}{49} =v\)

\(v=- \frac{9}{49}\)

\(\frac{v-9}{10v+6}=11 \\\\ 11(10v+6)=v-9 \\\\ 110v+66=v-9 \\\\ 110v-v=-9-66 \\\\ 109v= -75 \\\\ \boxed{v=-\frac{75}{109}}\)