Jasonwolf13
Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

\begin{tabular}{|l|l|}
\hline
Mathematical Statement & Justification \\
\hline
[tex]$4(x+5)=2 x+2$[/tex] & Given \\
\hline
[tex]$4 x+20=2 x+2$[/tex] & Distributive Property \\
\hline
[tex]$2 x+20=2$[/tex] & Subtraction Property of Equality \\
\hline
[tex]$2 x=-18$[/tex] & Subtraction Property of Equality \\
\hline
[tex]$x=-9$[/tex] & Division Property of Equality \\
\hline
\end{tabular}

Fill in the missing justifications in the correct order:

A. Distributive Property; Subtraction Property of Equality; Subtraction Property of Equality; Division Property of Equality
B. Distributive Property; Subtraction Property of Equality; Division Property of Equality; Subtraction Property of Equality
C. Subtraction Property of Equality; Addition Property of Equality; Distributive Property; Division Property of Equality
D. Subtraction Property of Equality; Distributive Property; Addition Property of Equality; Division Property of Equality

Sagot :

GinnyAnswer
To solve the given equation step-by-step and provide the correct justifications, let's break down the process:

1. Start with the given equation:
[tex]\[ 4(x + 5) = 2x + 2 \][/tex]
Justification: Given

2. Apply the Distributive Property to the left-hand side of the equation to expand it:
[tex]\[ 4x + 20 = 2x + 2 \][/tex]
Justification: Distributive Property

3. Subtract [tex]\(2x\)[/tex] from both sides of the equation to move the variable terms to one side:
[tex]\[ 2x + 20 = 2 \][/tex]
Justification: Subtraction Property of Equality

4. Subtract 20 from both sides of the equation to isolate the variable term:
[tex]\[ 2x = -18 \][/tex]
Justification: Subtraction Property of Equality

5. Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = -9 \][/tex]
Justification: Division Property of Equality

Given these steps, let's fill in the missing justifications in the provided table:

[tex]\[ \begin{tabular}{|l|l|} \hline Mathematical Statement & Justification \\ \hline $4(x+5)=2 x+2$ & Given \\ \hline $4x+20=2x+2$ & Distributive Property \\ \hline $2x+20=2$ & Subtraction Property of Equality \\ \hline $2x=-18$ & Subtraction Property of Equality \\ \hline $x=-9$ & Division Property of Equality \\ \hline \end{tabular} \][/tex]

So, the correct order of justifications is:
Distributive Property, Subtraction Property of Equality, Subtraction Property of Equality, Division Property of Equality
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.