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What is the reason for each step in the solution of the equation?

[tex]\[
\begin{array}{c}
-6x = -2(x + 12) & \text{Given} \\
-6x = -2x - 24 & \text{Distributive Property} \\
-4x = -24 & \text{Addition Property of Equality} \\
x = 6 & \text{Division Property of Equality} \\
\end{array}
\][/tex]

Drag and drop the reasons into the boxes to correctly complete the table:

- Given
- Distributive Property
- Addition Property of Equality
- Division Property of Equality

Sagot :

GinnyAnsweridn
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]
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