Answer
$m=21/9$
Work Step by Step
We start by creating a common denominator for all of the fractions:
$\frac{10}{15}+\frac{9m}{15}=\frac{31}{15}$
We now can combine the denominators on the same side of the equation:
$\frac{10+9m}{15}=\frac{31}{15}$
We then multiply both sides by 15 to find:
$10+9m=31$
We subtract 10 and divide by 9 to obtain that $m=21/9$.
We plug 21/9 in for m and confirm that our answer is, indeed, correct.
