Using Algebraic Properties

Question

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: 8x/8=32/8


=



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 PropertyMultiplication Property
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Answer 1

Let's analyze the steps and identify the appropriate properties for your questions.

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

In Step 1, you have: \[ 6x + 2(x - 1) = 30 \] becomes: \[ 6x + 2x - 2 = 30 \]

Here, you are distributing \(2\) to both terms inside the parentheses \((x - 1)\). Thus, the property that justifies this operation is the Distributive Property.

Correct Response: A. Distributive Property

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

In Step 3, you have: \[ 8x - 2 = 30 \] and you add \(2\) to both sides of the equation to get: \[ 8x - 2 + 2 = 30 + 2 \]

This operation involves adding the same value (\(+2\)) to both sides of the equation. This is justified by the Addition Property of Equality.

Correct Response: B. Addition Property

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In summary:

1. Step 1 is justified by the Distributive Property.
2. Step 3 is justified by the Addition Property of Equality.