Let's analyze the steps and provide the appropriate reasons for each one:
-
Step: \( 3(4x - 2) = - 30 \)
Reason: Given equation. -
Step: \( 12x - 6 = - 30 \)
Reason: Distributive Property (distributing 3 to both terms inside the parentheses). -
Step: \( 12x - 6 + 6 = - 30 + 6 \)
Reason: Addition Property of Equality (adding 6 to both sides of the equation). -
Step: \( 12x = - 24 \)
Reason: Simplification (combining like terms on both sides of the equation). -
Step: \( \frac{12x}{12} = \frac{-24}{12} \)
Reason: Division Property of Equality (dividing both sides by 12). -
Step: \( x = -2 \)
Reason: Simplification (simplifying both sides to find the value of \( x \)).
So, here are the completed justifications:
- Given equation.
- Distributive Property.
- Addition Property of Equality.
- Simplification.
- Division Property of Equality.
- Simplification.