#### Answer

$2$

#### Work Step by Step

Multiply by 10 (the LCD of the fractions) on both sides of the equation to obtain:
$10(\frac{x}{2}-\frac{1}{10}) = 10(\frac{x}{5}+\frac{1}{2})
\\\frac{10x}{2} -\frac{10}{10}= \frac{10x}{5} + \frac{10}{2}
\\5x -1= 2x+5$
Subtract by $2x$ on both sides of the equation to obtain:
$3x-1=5$
Add $1$ to both sides of the equation to obtain:
$3x=6$
Divide by 3 on both sides of the equation to obtain:
$x = \frac{6}{3}
\\x=2$