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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

1 answer

For your questions:

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

Response: A Distributive Property
In Step 1, you apply the Distributive Property to expand \( 2(x - 1) \) into \( 2x - 2 \).

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

Response: B Addition Property
In Step 3, you are adding 2 to both sides of the equation to isolate the term with \( x \), which is justified by the Addition Property of Equality.

So, to summarize:

  • Question 1: A (Distributive Property)
  • Question 2: B (Addition Property)