IDNLearn.com: Where your questions meet expert answers and community support. Ask your questions and receive comprehensive, trustworthy responses from our dedicated team of experts.

\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 :

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
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.