#### Answer

$5$

#### Work Step by Step

For easier work, it is better to get rid of the fractions.
This can be achieved by multiplying the LCD of $10$ on both sides of the equation to obtain:
$10(\frac{3x}{5}) - x = 10(\frac{x}{10}-\frac{5}{2})
\\\frac{30x}{5} - 10x = \frac{10x}{10} - \frac{50}{2}
\\6x - 10x = x-25
\\-4x = x-25$
Add $4x$ and $25$ on both sides to obtain:
$25=x+4x
\\25=5x
\\\frac{25}{5}=\frac{5x}{5}
\\5 = x$
Check:
$\begin{array}{ccc}
&\frac{3(5)}{5} - 5&= &\frac{5}{10}-\frac{5}{2}
\\&\frac{15}{5}-5 &= &\frac{1}{2}-\frac{5}{2}
\\&3-5 &= &-\frac{4}{2}
\\&-2 &= &-2\end{array}$