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
