Question

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 PropertyMultiplication Property
Question 2
Identify the property that justifies Step 3 when solving the given equation.
Responses
A Reflexive PropertyReflexive Property
B Addition Property Addition Property
C Substitution PropertySubstitution Property
D Multiplication Property

Answer 1

**Question 1: Identify the property that justifies Step 1 when solving the given equation.**

Step 1 shows the distribution of 2 across the terms inside the parentheses:
\[ 6x + 2(x - 1) = 6x + 2x - 2. \]
The appropriate property that justifies this step is the **Distributive Property**.

**Correct Answer: A Distributive Property**

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**Question 2: Identify the property that justifies Step 3 when solving the given equation.**

In Step 3, we see the addition of 2 to both sides of the equation:
\[ 8x - 2 + 2 = 30 + 2. \]
This step is justified by the principle that states when you add the same value to both sides of an equation, the equation remains balanced. This is called the **Addition Property of Equality**.

**Correct Answer: B Addition Property**