It is given that 2(3 + x) = 6 + 2x. This is an example of the _ property.
A. associative
B. commutative
C. distributive
D. identity
C. distributive
This is an example of the distributive property.
To determine which property is being illustrated in the given equation, let's first simplify the equation itself:
2(3 + x) = 6 + 2x
To simplify the left side of the equation, we apply the distributive property, which states that for any numbers a, b, and c, a(b + c) = ab + ac. In our equation, a = 2, b = 3, and c = x. Applying the distributive property, we get:
2 * 3 + 2 * x = 6 + 2x
Now simplifying both sides of the equation:
6 + 2x = 6 + 2x
We can observe that both sides of the equation are equal.
This signifies that the original equation is an example of the identity property.
The identity property states that for any number x, x + 0 = x. In our equation, x + 0 is represented by 6 + 2x, which is equal to 6 + 2x itself. Therefore, the correct answer is D. identity.