SOLUTION: if a is an integer, which of the following is always an odd integer? (a)4a+2 (b)10a (c)8a+1 (d).83 please help!!!!!!

Question 214411This question is from textbook algebra 1 an integrated approach
: if a is an integer, which of the following is always an odd integer?

(a)4a+2 (b)10a (c)8a+1 (d).83
please help!!!!!! This question is from textbook algebra 1 an integrated approach

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Recall that if 'k' is an integer, then is ALWAYS odd. Why? The number is ALWAYS even (because all even integers are a multiple of 2). If you add 1 to an even integer, you will get an odd integer. So this shows us that is ALWAYS odd where 'k' is an integer.

So the goal is to try to transform each choice into either the form (even form) or (odd form).

a)

Start with the given expression

Factor out the GCF 2

Replace 'a+1' with 'k' (which is an integer)

So is ALWAYS even (try plugging in some integers for 'a' to test this).

-----------------------------
b)

We can rewrite as which can come to (where . So is ALWAYS even.

-----------------------------
c)

We can rewrite as and then let . Now replace '4a' with 'k' to get . So (where )

This shows us that is ALWAYS odd.

-----------------------------
d)

The value 0.83 is neither even nor odd. Why is this? A number can only be even or odd when it is a whole number or integer. Since 0.83 is NOT a whole number, it is neither even nor odd.

So to recap, the only odd integer of the group is
RELATED QUESTIONS
If y is an integer,which of the following is always an even integer? (a) y + 1 (b)... (answered by neatmath,richard1234)

If a is an even integer and b is an odd integer, which of the following must be even?... (answered by mananth)

if k is a positive integer, which of the following must represent an even integer that is (answered by sudhanshu_kmr)

if n is an odd integer, which expression always represents an odd integer? (A) (2n - (answered by Alan3354)

If n is an integer, which of the following represents an odd number? (A) 2n+3 (B) 2n (answered by Alan3354)

If the ratio of two positive integers is 3 to 2,which of the following statements about... (answered by Alan3354)

If m is an odd integer, which expression always represents an odd integer? A) 3^m - 1 (answered by richard1234)

If x is an odd integer, which of the following must also be an odd integer? a.x+1 b.2x (answered by josgarithmetic)

if (x+3)/2 is an integer, then x must be A. a negative integer B. a positive integer (answered by Edwin McCravy)