The reciprocal of $\frac{3}{10}$ is $\left(\frac{1}{x}+1\right)$. What is the value of $x$ ?
(A) $\frac{7}{3}$
(B) $\frac{3}{13}$
(C) $\frac{3}{7}$
(D) $\frac{5}{3}$
(E) $\frac{3}{5}$
Since the reciprocal of $\frac{3}{10}$ is $\left(\frac{1}{x}+1\right)$, then

$$
\begin{aligned}
\frac{1}{x}+1 & =\frac{10}{3} \\
\frac{1}{x} & =\frac{7}{3} \\
x & =\frac{3}{7}
\end{aligned}
$$

so $x=\frac{3}{7}$.