jmc

We let the numerator be $x$, so the denominator is $3x-7$. Because the fraction equals $2/5$, we have $x/(3x-7)=2/5$. Multiplying both sides by $5(3x-7)$ (or cross-multiplying) gives $5x=2(3x-7)$. Expanding the right side gives $5x=6x-14$. Subtracting $6x$ from both sides gives $-x=-14$, so we find $x=\boxed{14}$.