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Complete the Proof

Complete the following proof by choosing the correct reason for each statement.

[tex]\[
\begin{tabular}{|l|l|}
\hline
Statement & Reason \\
\hline
\(\frac{(4x+6)}{2}=9\) & Given \\
\hline
\(4x + 6 = 18\) & Multiplication Property of Equality \\
\hline
\(4x = 12\) & Subtraction Property of Equality \\
\hline
\(x = 3\) & Division Property of Equality \\
\hline
\end{tabular}
\][/tex]

Reason choices:

- Multiplication Property of Equality
- Subtraction Property of Equality
- Division Property of Equality
- Simplify
- Given
- Distributive Property
- Substitution Property of Equality



Answer :

GinnyAnswer
To complete the proof, we'll use the correct reasons for each step based on standard algebraic properties:

\begin{tabular}{|l|l|}
\hline
Statement & Reason \\
\hline
[tex]$\frac{(4 x+6)}{2}=9$[/tex] & Given \\
\hline
[tex]$4 x + 6 = 18$[/tex] & Multiplication Property of Equality \\
\hline
[tex]$4 x = 12$[/tex] & Subtraction Property of Equality \\
\hline
[tex]$x = 3$[/tex] & Division Property of Equality \\
\hline
\end{tabular}

Thus, the proof is completed by correctly applying the properties of equality:

1. The Multiplication Property of Equality allows us to multiply both sides of the equation by 2 to eliminate the fraction.
2. The Subtraction Property of Equality lets us subtract 6 from both sides to isolate the term with the variable.
3. The Division Property of Equality enables us to divide both sides by 4 to solve for [tex]\( x \)[/tex].

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