Let's complete the proof step-by-step and provide the reasons accordingly.
### Given Equation
The initial equation is:
[tex]\[ 12 = \frac{1}{3}x + 5 \][/tex]
Reason: Given
### Step 1: Subtract 5 from both sides
[tex]\[ 12 - 5 = \frac{1}{3}x \][/tex]
[tex]\[ 7 = \frac{1}{3}x \][/tex]
Reason: Subtraction Property of Equality
### Step 2: Multiply both sides by 3
[tex]\[ 7 \times 3 = \left(\frac{1}{3}x\right) \times 3 \][/tex]
[tex]\[ 21 = x \][/tex]
Reason: Multiplication Property of Equality
### Step 3: Write x on the left-hand side
[tex]\[ x = 21 \][/tex]
Reason: Symmetric Property of Equality
So, putting it all together in a tabular format, we have:
[tex]\[
\begin{tabular}{|l|l|}
\hline \text{Statement} & \text{Reason} \\
\hline 12 = \frac{1}{3} x + 5 & \text{Given} \\
\hline 7 = \frac{1}{3} x & \text{Subtraction Property of Equality} \\
\hline 21 = x & \text{Multiplication Property of Equality} \\
\hline x = 21 & \text{Symmetric Property of Equality} \\
\hline
\end{tabular}
\][/tex]
This completes the proof that if [tex]\( 12 = \frac{1}{3}x + 5 \)[/tex], then [tex]\( x = 21 \)[/tex].
