Sure, let's provide the correct justifications for each step in the solution:
\begin{tabular}{|r|l|}
\hline
Step & Justification \\
\hline
[tex]$\frac{17}{3} - \frac{3}{4} x = \frac{1}{2} x + 5$[/tex] & given \\
\hline
[tex]$\frac{17}{3} - \frac{3}{4} x - \frac{17}{3} = \frac{1}{2} x + 5 - \frac{17}{3}$[/tex] & subtraction property of equality \\
\hline
[tex]$-\frac{3}{4} x - \frac{1}{2} x = \frac{1}{2} x - \frac{2}{3} x - \frac{2}{3} - \frac{1}{2} x$[/tex] & simplification \\
\hline
[tex]$-\frac{5}{4} x = \frac{2}{3} x - \frac{4}{3} = -\frac{4}{3}$[/tex] & simplification \\
\hline
[tex]$x = \frac{8}{15} x$[/tex] & simplification \\
\hline
\end{tabular}
This breakdown aligns with the steps and justifications derived from reasoning about the equation.