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Sagot :
Let's fill in the missing pieces in your proof step-by-step.
Given: \(7(x-1)=2(3x+2)\)
[tex]\[ \begin{tabular}{|c|c|} \hline \text{Statement} & \text{Reason} \\ \hline 7(x-1)=2(3x+2) & \text{Given} \\ \hline 7(x - 1) = 2(3x + 2) & \text{Given} \\ \hline 7x - 7 = 6x + 4 & \text{Distributive Property (Expansion)} \\ \hline 7x - 7 = 6x + 4 & \text{4. Expand both sides} \\ \hline 7x - 6x - 7 = 6x - 6x + 4 & \text{Subtract } 6x \text{ from both sides} \\ \hline x - 7 = 4 & \text{Combine like terms} \\ \hline x - 7 + 7 = 4 + 7 & \text{Add 7 to both sides} \\ \hline x = 11 & \text{Solve for } x \\ \hline 11 = x & \text{Reflexive Property} \\ \hline \end{tabular} \][/tex]
Thus, the completed proof table is as follows:
[tex]\[ \begin{tabular}{|c|c|} \hline \text{Statement} & \text{Reason} \\ \hline 7(x-1)=2(3x+2) & \text{Given} \\ \hline 7x - 7 = 6x + 4 & \text{Expand both sides} \\ \hline x - 7 = 4 & \text{Subtract 6x from both sides} \\ \hline x = 11 & \text{Add 7 to both sides} \\ \hline 11 = x & \text{Reflexive Property} \\ \hline \end{tabular} \][/tex]
By following these steps and completing the proof table, we demonstrate that [tex]\(x = 11\)[/tex].
Given: \(7(x-1)=2(3x+2)\)
[tex]\[ \begin{tabular}{|c|c|} \hline \text{Statement} & \text{Reason} \\ \hline 7(x-1)=2(3x+2) & \text{Given} \\ \hline 7(x - 1) = 2(3x + 2) & \text{Given} \\ \hline 7x - 7 = 6x + 4 & \text{Distributive Property (Expansion)} \\ \hline 7x - 7 = 6x + 4 & \text{4. Expand both sides} \\ \hline 7x - 6x - 7 = 6x - 6x + 4 & \text{Subtract } 6x \text{ from both sides} \\ \hline x - 7 = 4 & \text{Combine like terms} \\ \hline x - 7 + 7 = 4 + 7 & \text{Add 7 to both sides} \\ \hline x = 11 & \text{Solve for } x \\ \hline 11 = x & \text{Reflexive Property} \\ \hline \end{tabular} \][/tex]
Thus, the completed proof table is as follows:
[tex]\[ \begin{tabular}{|c|c|} \hline \text{Statement} & \text{Reason} \\ \hline 7(x-1)=2(3x+2) & \text{Given} \\ \hline 7x - 7 = 6x + 4 & \text{Expand both sides} \\ \hline x - 7 = 4 & \text{Subtract 6x from both sides} \\ \hline x = 11 & \text{Add 7 to both sides} \\ \hline 11 = x & \text{Reflexive Property} \\ \hline \end{tabular} \][/tex]
By following these steps and completing the proof table, we demonstrate that [tex]\(x = 11\)[/tex].
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