It is given that 2(3 + x) = 6 + 2x. This is an example of the ___________ property.
Responses
A associativeassociative
B commutativecommutative
C distributivedistributive
D identityidentity
C distributive
This is an example of the distributive property.
C. distributive
To determine the property being demonstrated in the given equation, we need to examine how the terms are being manipulated.
In this equation, the expression on the left side, 2(3 + x), is being distributed to both the 3 and the x within the parentheses.
The distributive property states that when we multiply a number by the sum of two numbers in parentheses, we can distribute the multiplication to each term within the parentheses.
The equation 2(3 + x) can be rewritten as 2 * 3 + 2 * x because we distribute the multiplication. This simplifies to 6 + 2x.
The equation given, 2(3 + x) = 6 + 2x, demonstrates the distributive property in action. Therefore, the answer is C. distributive.