Jasonwolf13
Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Get precise and detailed answers to your questions from a knowledgeable 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 this helpful. Feel free to come back anytime for more accurate answers and updated information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.