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Complete the missing reasons for the proof.

Given: [tex]4(x-2)=6x+18[/tex]

Prove: [tex]x=-13[/tex]

\begin{tabular}{|c|c|}
\hline
Statements & Reasons \\
\hline
1. [tex]4(x-2)=6x+18[/tex] & Given \\
\hline
2. [tex]4x-8=6x+18[/tex] & Distributive property \\
\hline
3. [tex]-2x-8=18[/tex] & Subtraction property of equality \\
\hline
4. [tex]-2x=26[/tex] & Addition property of equality \\
\hline
5. [tex]x=-13[/tex] & Division property of equality \\
\hline
\end{tabular}

A. Subtraction property of equality; Division property of equality
B. Addition property of equality; Division property of equality
C. Subtraction property of equality; Multiplication property of equality
D. Addition property of equality; Multiplication property of equality

Sagot :

GinnyAnswer
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
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