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Elani signed up for an installment plan with [tex]$0 \%$[/tex] interest to purchase a new couch that costs [tex]$\$[/tex] 770[tex]$. She creates an equation to model the situation, where $[/tex]x[tex]$ represents the number of months and $[/tex]y[tex]$ represents the balance of the installment account:
\[ y = 770 - 55x \]

Determine the missing steps and justifications in the solution.
\[
\begin{array}{l}
\text{subtraction property of equality} \\
y - 770 = -55x \\
\frac{y - 770}{-55} = x \\
\frac{y - 770}{55} = -x \\
y - 770 = -715x \\
\text{addition property of equality} \\
\end{array}
\]

\begin{tabular}{|c|l|}
\hline
Steps & \multicolumn{1}{|c|}{Justification} \\
\hline
$[/tex]y = 770 - 55x[tex]$ & given \\
\hline
$[/tex]y - 770 = 770 - 55x - 770[tex]$ & subtraction property of equality \\
\hline
$[/tex]y - 770 = -55x[tex]$ & simplification \\
\hline
$[/tex]\frac{y - 770}{-55} = x$ & multiplication property of equality \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Certainly! Let's fill in the missing steps and justifications based on the provided information.

Given the equation: [tex]\( y = 770 - 55x \)[/tex]

Determine the solution step by step with appropriate justifications:

[tex]\[ \begin{array}{|c|l|} \hline Steps & \multicolumn{1}{|c|}{ Justification } \\ \hline y = 770 - 55x & \text{given} \\ \hline y - 770 = 770 - 55x - 770 & \text{subtraction property of equality} \\ \hline y - 770 = -55x & \text{simplification} \\ \hline \frac{y - 770}{-55} = \frac{-55x}{-55} & \text{division property of equality} \\ \hline (y - 770) / -55 = x & \text{simplification} \\ \hline \end{array} \][/tex]

Each of these steps is justified as follows:
1. Given: The initial equation representing the relationship between the elements (cost and number of installments).
2. Subtraction property of equality: Isolating the term with [tex]\( x \)[/tex] by subtracting 770 from both sides.
3. Simplification: Simplifying the right-hand side of the equation to effectively isolate all terms involving [tex]\( x \)[/tex].
4. Division property of equality: Dividing both sides by -55 to solve for [tex]\( x \)[/tex].
5. Simplification: The final step simplifies to show the expression for [tex]\( x \)[/tex].