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].
