Question

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Feature
Using Algebraic Properties
Solving the equation 6x + 2(x − 1) = 30

Given: 6x + 2(x − 1) = 30
Step 1: 6x + 2x − 2 = 30
Step 2: 8x − 2 = 30
Step 3: 8x − 2 + 2 = 30 + 2
Step 4:


=



Step 5: x = 4
Question 1
Identify the property that justifies Step 1 when solving the given equation.
Responses
A Distributive PropertyDistributive Property
B Substitution PropertySubstitution Property
C Symmetric PropertySymmetric Property
D Multiplication Property

Answer 1

The property that justifies Step 1 (where \(2(x - 1)\) is expanded to \(2x - 2\)) is the **Distributive Property**. In this step, the expression \(2(x - 1)\) is being distributed, which involves multiplying \(2\) by both \(x\) and \(-1\).

So the correct response is:

**A Distributive Property**