To solve this problem, we need to find the next larger even integer after the integer represented by [tex]\( n + 5 \)[/tex].
1. Understand the given integer:
- We are given that [tex]\( n + 5 \)[/tex] is an even integer.
2. Identify the pattern of even integers:
- Even integers follow a pattern where they increase by 2 for each subsequent even number. For instance, if one even integer is 6, the next even integer is 8, and so on. Hence, the difference between any two consecutive even integers is 2.
3. Determine the next larger even integer:
- Since [tex]\( n + 5 \)[/tex] is an even integer, the next even integer would be obtained by adding 2 to [tex]\( n + 5 \)[/tex].
- Mathematically, you can represent the next even integer as [tex]\( (n + 5) + 2 = n + 7 \)[/tex].
Therefore, the next larger even integer is [tex]\( n + 7 \)[/tex]. So, filling in the blank:
[tex]\[ n + 7 \][/tex]
