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The justification for each step in the solution to the given equation.

\begin{tabular}{|c|c|}
\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]$-\frac{3}{4} x = \frac{1}{2} x - \frac{2}{3}$[/tex] & Simplification \\
\hline
[tex]$-\frac{3}{4} x - \frac{1}{2} x = \frac{1}{2} x - \frac{2}{3} - \frac{1}{2} x$[/tex] & Subtraction property of equality \\
\hline
[tex]$-\frac{5}{4} x = -\frac{2}{3}$[/tex] & Simplification \\
\hline
[tex]$-\frac{5}{4} x \cdot -\frac{4}{5} = -\frac{2}{3} \cdot -\frac{4}{5}$[/tex] & Multiplication property of equality \\
\hline
[tex]$x = \frac{8}{15}$[/tex] & Simplification \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
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.
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