Jasonwolf13
Answered

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\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
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