Let's walk through the proof step by step and fill in the corresponding reasons.
\begin{tabular}{|l|l|}
\hline
\multicolumn{1}{|c|}{Statement} & Reason \\
\hline
[tex]$3 x+12=8 x-18$[/tex] & Given \\
\hline
[tex]$3 x-8 x+12=8 x-18-8 x$[/tex] & Addition Property of Equality \\
\hline
[tex]$-5 x+12=-18$[/tex] & Simplify \\
\hline
[tex]$-5 x+12-12=-18-12$[/tex] & Addition Property of Equality \\
\hline
[tex]$-5 x=-30$[/tex] & Simplify \\
\hline
[tex]$\frac{-5 x}{-5}=\frac{-30}{-5}$[/tex] & Division Property of Equality \\
\hline
[tex]$x=6$[/tex] & Simplify \\
\hline
\end{tabular}
Each statement follows logically from the previous one, and the reasons explain the mathematical operations or properties used to transition from one step to the next.
