Answer
$x=7$
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 $14$ on both sides of the equation to obtain:
$14(2x-\frac{2x}{7}) = 14(\frac{x}{2}+\frac{17}{2})
\\28x - \frac{28x}{7} = \frac{14x}{2} +\frac{14(17)}{2}
\\28x - 4x = 7x+7(17)
\\24x = 7x+119$
Subtract $7x$ on both sides to obtain:
$24x-7x=119
\\17x=119
\\\frac{17x}{17}=\frac{119}{17}
\\x = 7$
Check:
$\begin{array}{ccc}
&2(7)-\frac{2(7)}{7} &= &\frac{7}{2}+\frac{17}{2}
\\&14-\frac{14}{7} &= &\frac{24}{2}
\\&14-2 &= &12
\\&12 &= &12\end{array}$
