Answer
$n=\frac{9}{14}$
Work Step by Step
We will solve the equation by first finding the least common denominator on the left side of the equation and then cross multiplying the resultant expression:
$\frac{3n+1}{5}+\frac{n-2}{3}=\frac{2}{15}$
$\frac{3(3n+1)+5(n-2)}{15}=\frac{2}{15}$
$\frac{9n+3+5n-10}{15}=\frac{2}{15}$
$\frac{9n+5n-10+3}{15}=\frac{2}{15}$
$\frac{14n-7}{15}=\frac{2}{15}$
$15(14n-7)=2(15)$
$14n-7=2$
$14n=2+7$
$14n=9$
$n=\frac{9}{14}$
