Let's fill in the missing justifications step-by-step for the given mathematical statement, ensuring each step is properly justified.
We start with the given equation:
[tex]\[ 4(x+5)=2x+2 \][/tex]
1. We apply the Distributive Property to expand the left side:
[tex]\[ 4(x+5) = 4x + 20 \][/tex]
So, the justification here is "Distributive Property."
2. Next, we subtract [tex]\(2x\)[/tex] from both sides of the equation using the Subtraction Property of Equality:
[tex]\[ 4x + 20 - 2x = 2x + 2 - 2x \][/tex]
Simplifying this gives:
[tex]\[ 2x + 20 = 2 \][/tex]
So, the justification here is "Subtraction Property of Equality."
3. Then we subtract [tex]\(20\)[/tex] from both sides using the Subtraction Property of Equality:
[tex]\[ 2x + 20 - 20 = 2 - 20 \][/tex]
Simplifying this gives:
[tex]\[ 2x = -18 \][/tex]
So, the justification here is "Subtraction Property of Equality."
4. Finally, we divide both sides by 2 using the Division Property of Equality:
[tex]\[ \frac{2x}{2} = \frac{-18}{2} \][/tex]
Simplifying this yields:
[tex]\[ x = -9 \][/tex]
So, the justification here is "Division Property of Equality."
Therefore, the completed table with correct justifications is:
[tex]\[
\begin{tabular}{|l|l|}
\hline Mathematical Statement & Justification \\
\hline $4(x+5)=2 x+2$ & Given \\
\hline $4 x+20=2 x+2$ & Distributive Property \\
\hline $2 x+20=2$ & Subtraction Property of Equality \\
\hline $2 x=-18$ & Subtraction Property of Equality \\
\hline$x=-9$ & Division Property of Equality \\
\hline
\end{tabular}
\][/tex]
The correct order of justifications is:
- Distributive Property
- Subtraction Property of Equality
- Subtraction Property of Equality
- Division Property of Equality
