Find $x$, if $\frac{2x}{3}+1=\frac{7x}{15}+3$.

The correct option is D: $10$

Given: $\frac{2x}{3}+1=\frac{7x}{15}+3$.

Transposing $x$ terms to one side, we get

$\Rightarrow \frac{2x}{3}-\frac{7x}{15}=3-1$

L.C.M of $3,15$ is $15$.

$\Rightarrow \frac{2x\times 5}{3\times 5}-\frac{7x}{15}=3-1$

$\Rightarrow \frac{10x}{15}-\frac{7x}{15}=2$

$\Rightarrow \frac{10x-7x}{15}=2$

$\Rightarrow \frac{3x}{15}=2$

$\therefore x=\frac{30}{3}=10$.