Solving the equation 6x + 2(x − 1) = 30

Question

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





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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

Let's analyze the steps you provided to answer the questions.

Question 1

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

In Step 1, you expand the expression \(2(x - 1)\) using the distributive property. This is the property that states \(a(b + c) = ab + ac\).

So, the correct answer is: 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 add \(2\) to both sides of the equation \(8x - 2 = 30\). This step relies on the addition property of equality, which states that if you add the same number to both sides of an equation, the equality is maintained.

So, the correct answer is: B. Addition Property

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In summary:

1. Question 1: A. Distributive Property
2. Question 2: B. Addition Property