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The equation 3(4x - 2) = - 30 is solved in several steps below. For each step, choose the reason that best justifies it. Step Reason X 5 3(4x - 2) = - 30 Given equation 12x - 6 = - 30 "Choose one" 12x - 6 + 6 = - 30 + 6 "Choose one" 12x = - 24 "Choose one" (12x)/12 = - 24/12 "Choose one" x = - 2 "Choose one"

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Let's analyze the steps and provide the appropriate reasons for each one:

  1. Step: \( 3(4x - 2) = - 30 \)
    Reason: Given equation.

  2. Step: \( 12x - 6 = - 30 \)
    Reason: Distributive Property (distributing 3 to both terms inside the parentheses).

  3. Step: \( 12x - 6 + 6 = - 30 + 6 \)
    Reason: Addition Property of Equality (adding 6 to both sides of the equation).

  4. Step: \( 12x = - 24 \)
    Reason: Simplification (combining like terms on both sides of the equation).

  5. Step: \( \frac{12x}{12} = \frac{-24}{12} \)
    Reason: Division Property of Equality (dividing both sides by 12).

  6. Step: \( x = -2 \)
    Reason: Simplification (simplifying both sides to find the value of \( x \)).

So, here are the completed justifications:

  1. Given equation.
  2. Distributive Property.
  3. Addition Property of Equality.
  4. Simplification.
  5. Division Property of Equality.
  6. Simplification.