Using Algebraic Properties Solving the equation $$ 6 x+2(x-1)=30 $$ Given: $$ 6 x+2(x-1)=30 $$ Step 1: $$ 6 x+2 x-2=30 $$ Step 2: $$ 8 x-2=30 $$ Step 3: $$ 8 x-2+2=30+2 $$ Step 4: $$ \frac{8 x}{8}=\frac{32}{8} $$ Step 5: $$ x=4 $$ Identify the property that justifies Step 1 wher equation. A Distributive Property B Substitution Property C Symmetric Property D Multiplication Property Identify the property that justifies Step 3 when equation.

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**Step 1 Justification:**

In Step 1, the equation transforms from $$ 6x + 2(x - 1) = 30 $$ to $$ 6x + 2x - 2 = 30 $$. This transformation involves distributing the multiplication of 2 across the terms inside the parentheses.

- **Distributive Property:** This property states that $$ a(b + c) = ab + ac $$. Here, $$ 2(x - 1) $$ is distributed to become $$ 2x - 2 $$.

**Answer:**  
**A. Distributive Property**

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**Step 3 Justification:**

In Step 3, the equation changes from $$ 8x - 2 = 30 $$ to $$ 8x - 2 + 2 = 30 + 2 $$. This step involves adding the same number to both sides of the equation to maintain equality.

- **Addition Property of Equality:** This property states that if you add the same number to both sides of an equation, the equality remains true. Here, 2 is added to both sides to isolate the variable term.

**Answer:**  
**Addition Property of Equality**
**Step 1 Justification:** A. Distributive Property **Step 3 Justification:** Addition Property of Equality

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