dentify 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 Property
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
A Distributive Property
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
B Addition Property
The property that justifies Step 1 in solving the given equation is the Distributive Property. The Distributive Property states that for any real numbers a, b, and c:
a(b + c) = ab + ac
In Step 1 of solving the equation, the Distributive Property is used to distribute the 2 to both terms inside the parentheses:
6x + 2(x − 1) = 30
6x + 2 * x - 2 * 1 = 30
This simplifies to:
6x + 2x - 2 = 30
So the answer is: A) Distributive Property