Problem 83 - College Algebra

Question

What is an identity? Give an example.

Step-by-Step Solution

Answer

An identity is an equality that holds true for any values of its variables. An example of an identity is \(2*(x + y) = 2*x + 2*y\)

Step 1: Definition of Identity

An identity is an equality that remains true regardless of the values of any variables that appear within it. They are the foundational elements of mathematics and critical in various areas such as algebra. For example: the identity for addition involves the number zero (a + 0 = a), and for multiplication, it's the number one (a * 1 = a). These are named as the additive identity and multiplicative identity respectively.

Step 2: Provide an example

Let's consider a simple example of an identity. An identity in algebra could be \(2*(x + y) = 2*x + 2*y\). Regardless of the values you choose for x and y, both sides of this equation will always remain equal.