Certainly, let's complete the proof by filling in the correct reasons for each step.
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|}{Statement} & \multicolumn{1}{|c|}{Reason} \\
\hline [tex]$4x = 12x + 32$[/tex] & Given \\
\hline [tex]$-8x = 32$[/tex] & Subtraction Property of Equality \\
\hline [tex]$x = -4$[/tex] & Division Property of Equality \\
\hline
\end{tabular}
Here is the detailed step-by-step solution in words:
1. Given: The initial equation is given as [tex]\( 4x = 12x + 32 \)[/tex].
2. Subtraction Property of Equality: To isolate the term with [tex]\( x \)[/tex] on one side, subtract [tex]\( 12x \)[/tex] from both sides of the equation:
[tex]\[ 4x - 12x = 32 \][/tex]
[tex]\[ -8x = 32 \][/tex]
3. Division Property of Equality: Finally, to solve for [tex]\( x \)[/tex], divide both sides of the equation by [tex]\(-8\)[/tex]:
[tex]\[ x = \frac{32}{-8} \][/tex]
[tex]\[ x = -4 \][/tex]
So, each step is justified with the appropriate property of equality used during that step.
