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

\begin{tabular}{|c|l|}
\hline
Step & Justification \\
\hline
[tex]$\frac{17}{3}-\frac{3}{4} x=\frac{1}{2} x+5$[/tex] & \\
\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}



Answer :

GinnyAnswer
Certainly! Let's provide the justifications for each step in solving the given equation:

1. Initial Equation:
[tex]\[ \frac{17}{3} - \frac{3}{4} x = \frac{1}{2} x + 5 \][/tex]
Justification: Given Equation

2. Subtract [tex]\(\frac{17}{3}\)[/tex] from both sides:
[tex]\[ \frac{17}{3} - \frac{3}{4} x - \frac{17}{3} = \frac{1}{2} x + 5 - \frac{17}{3} \][/tex]
Justification: Subtraction property of equality

3. Simplify:
[tex]\[ -\frac{3}{4} x = \frac{1}{2} x - \frac{2}{3} \][/tex]
Justification: Simplification

4. Subtract [tex]\(\frac{1}{2} x\)[/tex] from both sides:
[tex]\[ -\frac{3}{4} x - \frac{1}{2} x = \frac{1}{2} x - \frac{2}{3} - \frac{1}{2} x \][/tex]
Justification: Subtraction property of equality

5. Simplify:
[tex]\[ -\frac{5}{4} x = -\frac{2}{3} \][/tex]
Justification: Simplification

6. Multiply both sides by [tex]\(-\frac{4}{5}\)[/tex]:
[tex]\[ -\frac{5}{4} x \cdot -\frac{4}{5} = -\frac{2}{3} \cdot -\frac{4}{5} \][/tex]
Justification: Multiplication property of equality

7. Simplify:
[tex]\[ x = \frac{8}{15} \][/tex]
Justification: Simplification

To summarize, the step-by-step justifications are:

1. Given Equation
2. Subtraction property of equality
3. Simplification
4. Subtraction property of equality
5. Simplification
6. Multiplication property of equality
7. Simplification

This organizes the justifications corresponding to each step in the solution process.

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