jmc

In order to combine the fraction and the integer into a single fraction, we write $2$ as a fraction with a denominator of $7$, or $\frac{14}{7}$. We get $$\frac{4+3c}{7}+\frac{14}{7}=\frac{4+3c+14}{7}=\boxed{\frac{18+3c}{7}}.$$