1. The problem asks for the additive inverse of $-\frac{3}{7}$. 2. The additive inverse of a number $x$ is the number that, when added to $x$, results in zero. Mathematically, if $x$ is a number, its additive inverse is $-x$. 3. Given $x = -\frac{3}{7}$, the additive inverse is $-\left(-\frac{3}{7}\right)$. 4. Simplifying, $-\left(-\frac{3}{7}\right) = \frac{3}{7}$. 5. Therefore, the additive inverse of $-\frac{3}{7}$ is $\frac{3}{7}$.