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Which table shows the correct methods used to justify the solution steps?

[tex]
3(x-5)+7x=65
[/tex]

[tex]\[
\begin{tabular}{|c|c|}
\hline
\text{Solution Step} & \text{Method to Justify} \\
\hline
3x - 15 + 7x = 65 & \text{Division property of equality} \\
\hline
10x - 15 = 65 & \text{Combine like terms} \\
\hline
10x = 80 & \text{Distributive property} \\
\hline
x = 8 & \text{Addition property of equality} \\
\hline
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{|c|c|}
\hline
\text{Solution Step} & \text{Method to Justify} \\
\hline
3x - 15 + 7x = 65 & \text{Distributive property} \\
\hline
10x - 15 = 65 & \text{Combine like terms} \\
\hline
10x = 80 & \text{Addition property of equality} \\
\hline
x = 8 & \text{Division property of equality} \\
\hline
\end{tabular}
\][/tex]

Sagot :

GinnyAnswer
To solve the equation \( 3(x - 5) + 7x = 65 \) step-by-step, we need to apply mathematical properties correctly. Here are the steps and the methods used to justify each one:

1. Starting with the initial equation:
[tex]\[ 3(x - 5) + 7x = 65 \][/tex]

2. Distributive Property: Distribute the \( 3 \) across \( (x - 5) \):
[tex]\[ 3x - 15 + 7x = 65 \][/tex]
Justification Method: Distributive property.

3. Combine Like Terms: Combine \( 3x \) and \( 7x \):
[tex]\[ 10x - 15 = 65 \][/tex]
Justification Method: Combine like terms.

4. Addition Property of Equality: Add \( 15 \) to both sides to isolate the term with \( x \):
[tex]\[ 10x = 80 \][/tex]
Justification Method: Addition property of equality.

5. Division Property of Equality: Divide both sides by \( 10 \) to solve for \( x \):
[tex]\[ x = 8 \][/tex]
Justification Method: Division property of equality.

Based on the correctly applied steps and their justifying methods, we can identify the correct table:

[tex]\[ \begin{tabular}{|c|c|} \hline Solution Step & Method to Justify \\ \hline [tex]$3x - 15 + 7x = 65$[/tex] & distributive property \\
\hline
[tex]$10x - 15 = 65$[/tex] & combine like terms \\
\hline
[tex]$10x = 80$[/tex] & addition property of equality \\
\hline
[tex]$x = 8$[/tex] & division property of equality \\
\hline
\end{tabular}
\][/tex]

So, the correct table is the second one provided.
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