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.

The property that justifies Step 1 in the equation \( 6x + 2(x-1) = 30 \) is indeed the **Distributive Property**. This property allows you to distribute the \(2\) across the terms inside the parentheses, leading to the equation simplifying to \( 6x + 2x - 2 = 30 \). Now, for Step 3, where you are adding \(2\) to both sides of the equation, the property used here is known as the **Addition Property of Equality**. This property states that you can add the same number to both sides of an equation without changing the equality. So, \( 8x - 2 + 2 = 30 + 2\) maintains the balanced equation!