Sure! Below is a detailed justification for each step of the solution to the given equation.
[tex]\[
\begin{tabular}{|c|c|}
\hline Step & Justification \\
\hline
\frac{17}{3} - \frac{3}{4} x = \frac{1}{2} x + 5 & given \\
\hline
\begin{aligned}
\frac{17}{3} - \frac{3}{4} x - \frac{17}{3} = \frac{1}{2} x + 5 - \frac{17}{3}
\end{aligned} & subtraction property of equality \\
\hline
\begin{aligned}
-\frac{3}{4} x = \frac{1}{2} x - \frac{2}{3}
\end{aligned} & simplification \\
\hline
\begin{aligned}
-\frac{3}{4} x - \frac{1}{2} x = \frac{1}{2} x - \frac{2}{3} - \frac{1}{2} x
\end{aligned} & subtraction property of equality \\
\hline
\begin{aligned}
-\frac{5}{4} x = -\frac{2}{3}
\end{aligned} & simplification \\
\hline
-\frac{5}{4} x \cdot -\frac{4}{5} = -\frac{2}{3} \cdot -\frac{4}{5} & multiplication property of equality \\
\hline
\begin{aligned}
x= \frac{8}{15}
\end{aligned} & simplification \\
\hline
\end{tabular}
\][/tex]
These justifications show the application of mathematical properties to transform and solve the equation step-by-step.
