Let's work through the steps given, providing the correct justifications for each.
### Step-by-Step Solution:
1. Equation Given:
[tex]\[
\frac{17}{3}-\frac{3}{4} x = \frac{1}{2} x + 5
\][/tex]
2. Step 1: Move the constant term [tex]\(\frac{17}{3}\)[/tex] to the right side.
[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. Step 2: Simplify both sides.
[tex]\[
-\frac{3}{4} x = \frac{1}{2} x - \frac{2}{3}
\][/tex]
- Justification: Simplification
4. Step 3: Eliminate the variable term [tex]\(\frac{1}{2} x\)[/tex] on the right side.
[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. Simplified Result: (Exact expression not given, assuming this step involves further simplification)
- Justification: Simplification
### Filling in the Table:
\begin{tabular}{|c|l|}
\hline
\textbf{Step} & \textbf{Justification} \\
\hline
[tex]$\frac{17}{3}-\frac{3}{4} x=\frac{1}{2} x+5$[/tex] & Given equation \\
\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
\text{Simplified result here} & Simplification \\
\hline
\end{tabular}
In summary:
1. The subtraction property of equality is used to move terms across the equation.
2. Simplification combines like terms or simplifies expressions on each side of the equation.
Following these steps, we can systematically solve the given equation or verify the given steps as correct.
