Let's solve the equation [tex]\( -6x = -2(x+12) \)[/tex] step-by-step and provide the reasons for each transformation within the table:
1. Starting with the initial equation:
[tex]\[
-6x = -2(x + 12)
\][/tex]
Reason: Given
2. Apply the Distributive Property to [tex]\(-2(x + 12)\)[/tex]:
[tex]\[
-6x = -2x - 24
\][/tex]
Reason: Distributive Property
3. Add [tex]\(2x\)[/tex] to both sides using the Addition Property of Equality:
[tex]\[
-6x + 2x = -2x + 2x - 24
\][/tex]
Simplifying, we get:
[tex]\[
-4x = -24
\][/tex]
Reason: Addition Property of Equality
4. Divide both sides by [tex]\(-4\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-24}{-4}
\][/tex]
Simplifying, we get:
[tex]\[
x = 6
\][/tex]
Reason: Division Property of Equality
Let's fill in the table correctly:
[tex]\[
\begin{array}{c|c}
\text{Equation} & \text{Reason} \\
\hline
-6x = -2(x+12) & \text{Given} \\
-6x = -2x - 24 & \text{Distributive Property} \\
-4x = -24 & \text{Addition Property of Equality} \\
x = 6 & \text{Division Property of Equality} \\
\end{array}
\][/tex]
