Question

Put the steps in correct order to prove that if n is even, then 7n + 4 is even

(You must provide an answer before moving to the next part.)
Rank the options below.
Then 7n + 4 = 14k + 4 = 2(7k + 2).
Then 7n + 4 = 14k + 4 = 2(7k + 2). Open choices for matching
This is 2 times an integer, so it is even.
This is 2 times an integer, so it is even. Open choices for matching
Since n is even, it can be written as 2k for some integer k.

Answer 1

The order of steps to prove that 7n + 4 is even if n is even involves expressing n as 2k, substituting into 7n + 4, distributing 7, factoring out 2, and showing the result is 2 times an integer.

Step-by-step explanation:

To prove that if n is even, then 7n + 4 is even, we must put the steps in the correct order:

1. Since n is even, it can be written as 2k for some integer k.
2. Then 7n + 4 can be rewritten using the substitution n = 2k, which gives us 7(2k) + 4.
3. By distributing 7 across the parentheses, we have 14k + 4.
4. Now we can factor out a 2, resulting in 2(7k + 2).
5. This is 2 times an integer, so it is even.

By following these steps, we can easily demonstrate that if n is even, 7n + 4 will also be even, as it can be expressed in the form 2m, where m is an integer.