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: 8x8
= 328
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
B Addition Property
and the other one
A Distributive Property
Question 1: The property that justifies Step 1 when solving the given equation is the Distributive Property.
Question 2: The property that justifies Step 3 when solving the given equation is the Addition Property.
Question 1: The property that justifies Step 1 when solving the given equation is the Distributive Property.
Explanation: The Distributive Property states that for any real numbers a, b, and c, the equation a(b + c) = ab + ac holds true.
In Step 1, we have the expression 2(x - 1). To simplify it, we must distribute the 2 across the terms inside the parentheses, giving us 2x - 2. This is done in accordance with the Distributive Property.
Therefore, the correct answer is A) Distributive Property.
Question 2: The property that justifies Step 3 when solving the given equation is the Addition Property.
Explanation: The Addition Property states that for any real numbers a, b, and c, the equation a = b implies a + c = b + c.
In Step 3, we add 2 to both sides of the equation to isolate the variable. By doing so, we maintain the equality between both sides because we are adding the same value to both sides.
Therefore, the correct answer is B) Addition Property.