General Form of an Odd Integer

Video Explanation

Watch the video below for a clear explanation:

Solution

Question: For some integer q, every odd integer is of the form:

(a) q    (b) q + 1    (c) 2q    (d) 2q + 1

Key Concept

An odd integer is an integer that is not divisible by 2.

Step-by-Step Explanation

If q is any integer, then:

2q represents all even integers.

Adding 1 to an even integer gives an odd integer.

So, every odd integer can be written as 2q + 1.

Examples:

q = 0 → 2q + 1 = 1
q = 1 → 2q + 1 = 3
q = −1 → 2q + 1 = −1

Final Answer

✔ The correct form is 2q + 1.

✔ Correct option: (d) 2q + 1

Conclusion

Hence, for some integer q, every odd integer is always of the form 2q + 1.