Answered

IDNLearn.com helps you find the answers you need quickly and efficiently. Discover detailed and accurate answers to your questions from our knowledgeable and dedicated community members.

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}

Sagot :

GinnyAnsweridn
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.
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.