Certainly! Let's fill in the missing pieces in the proof step-by-step.
Given: [tex]\( 7(x-1)=2(3x+2) \)[/tex]
Prove: [tex]\( x=11 \)[/tex]
Here is the step-by-step solution completed in the proof table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
\text{Statement} & \text{Reason} \\
\hline
\( 7(x-1)=2(3x+2) \) & \text{Given} \\
\hline
\( 7x - 7 = 6x + 4 \) & \text{Distributive Property} \\
\hline
\( 7x - 6x - 7 = 6x - 6x + 4 \Rightarrow x - 7 = 4 \) & \text{Subtract \( 6x \) from both sides} \\
\hline
\( x - 7 + 7 = 4 + 7 \Rightarrow x = 11 \) & \text{Add 7 to both sides} \\
\hline
\end{tabular}
\][/tex]
Notice that the final statement and its corresponding reason were corrected from the initially provided conditions to match the calculations. This demonstrates a clear and organized approach to solving the given equation, ensuring all steps are logically justified.
