Let's go through the proof step-by-step and fill in the missing reasons:
Given: [tex]\(4(x-2)=6x+18\)[/tex]
To prove: [tex]\(x=-13\)[/tex]
Starting with the proof:
1. [tex]\(4(x-2)=6x+18\)[/tex] - given
2. [tex]\(4x-8=6x+18\)[/tex] - distributive property
3. [tex]\(-2x-8=18\)[/tex] - subtraction property of equality (After subtracting [tex]\(6x\)[/tex] from both sides)
4. [tex]\(-2x=26\)[/tex] - addition property of equality (After adding 8 to both sides)
5. [tex]\(x=-13\)[/tex] - division property of equality (After dividing both sides by [tex]\(-2\)[/tex])
So, our complete table should be:
[tex]\[
\begin{tabular}{|c|c|}
\hline
Statements & Reasons \\
\hline
1. \(4(x-2)=6x+18\) & given \\
\hline
2. \(4x-8=6x+18\) & distributive property \\
\hline
3. \(-2x-8=18\) & subtraction property of equality \\
\hline
4. \(-2x=26\) & addition property of equality \\
\hline
5. \(x=-13\) & division property of equality \\
\hline
\end{tabular}
\][/tex]
Thus, the correct answer to fill in the blanks are:
- 3: subtraction property of equality
- 5: division property of equality
