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Drag each tile to the correct location on the table. Each tile can be used more than once, but not all tiles will be used.

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

- simplification
- multiplication property of equality
- addition property of equality
- subtraction property of equality
- division property of equality

\begin{tabular}{|c|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]$-\frac{3}{4} x=\frac{1}{2} x-\frac{2}{3}$[/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! Let's organize the steps and provide the correct justifications for each step of the solution.

\begin{tabular}{|c|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]$-\frac{3}{4} x=\frac{1}{2} x-\frac{2}{3}$[/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}

This structure shows each step of the solution with the appropriate justification for each transformation.
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