If n is an odd integer, which of the following is always even?

If n is an odd integer, which of the following is always even?

Correct Answer: 2n

Step 1: Understand that an odd integer n can be represented as n = 2k + 1, where k is an integer.
Step 2: Calculate n + 1. If n = 2k + 1, then n + 1 = 2k + 1 + 1 = 2k + 2 = 2(k + 1), which is even.
Step 3: Calculate n - 1. If n = 2k + 1, then n - 1 = 2k + 1 - 1 = 2k = 2k, which is also even.
Step 4: Calculate 2n. If n = 2k + 1, then 2n = 2(2k + 1) = 4k + 2 = 2(2k + 1), which is even.
Step 5: Conclude that both n + 1, n - 1, and 2n are always even when n is an odd integer.

Odd and Even Integers – Understanding the properties of odd and even integers, specifically how adding or subtracting 1 from an odd integer results in an even integer, and that multiplying an integer by 2 always yields an even integer.