If $\frac{x-3}{5}-2=\frac{2 x}{5}$, find the value of $x$.

Given: $\frac{x-3}{5}-2=\frac{2x}{5}$

To do: To find the value of $x$.

Given,

$\frac{x-3}{5}-2=\frac{2x}{5}$

​$\Rightarrow \frac{x-3-10}{5}=\frac{2x}{5}$      [Cross-multiplying the denominators on the LHS]

$\Rightarrow \frac{x-13}{5}=\frac{2x}{5}$

​

$\Rightarrow x-13=2x$                          [Multiplying $5$ on both sides]

$\Rightarrow 2x-x=-13$                         [Transposing $x$ terms to one side]

$\Rightarrow x=-13$

Thus, $x=-13$.