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Justify each step in solving the equation [tex]$4x = 7(x - 3)$[/tex] by writing a reason for each statement.

Answer:
\begin{tabular}{|c|c|}
\hline
Statement & Reason \\
\hline
1. [tex]$4x = 7(x - 3)$[/tex] & Given \\
\hline
2. [tex]$4x = 7x - 21$[/tex] & Distribute 7 to both terms inside the parentheses \\
\hline
3. [tex]$4x - 7x = -21$[/tex] & Subtract [tex]$7x$[/tex] from both sides \\
\hline
4. [tex]$-3x = -21$[/tex] & Combine like terms \\
\hline
5. [tex]$x = 7$[/tex] & Divide both sides by [tex]$-3$[/tex] \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Certainly! Let's walk through the solution of the equation [tex]\(4x = 7(x - 3)\)[/tex] step-by-step, justifying each step.

[tex]\[ \begin{tabular}{|c|c|} \hline \text{Statement} & \text{Reason} \\ \hline 1. \(4x = 7(x - 3)\) & 1. \text{Given equation} \\ \hline 2. \(4x = 7x - 21\) & 2. \text{Distribute 7 to the terms inside the parenthesis} \\ \hline 3. \(4x - 7x = -21\) & 3. \text{Subtract \(7x\) from both sides to isolate \(x\) terms on one side} \\ \hline 4. \(-3x = -21\) & 4. \text{Combine like terms on the left side} \\ \hline 5. \(x = 7\) & 5. \text{Divide both sides by -3 to solve for \(x\)} \\ \hline \end{tabular} \][/tex]

This thorough approach ensures that each step has a clear reason, facilitating understanding of the solution process.

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