#### Answer

The equation has one solution, $\frac{1}{3}$.

#### Work Step by Step

$\frac{v+2}{v}+\frac{4}{3v}=11$
$\frac{3(v+2)}{3v}+\frac{4}{3v}-\frac{11*3v}{3v}=0$
$\frac{3v+6+4-33v}{3v}=0$
$\frac{10-30v}{3v}=0$
$10-30v=0*3v$
$10-30v=0$
$30v=10$
$v=\frac{1}{3}$
Check:
$\frac{1/3+2}{1/3}+4/(3\times1/3)=7+4=11$
The equation has one solution, $\frac{1}{3}$.