Question

Write whether every positive integer can be the form of 4q+2,where q is an integer. Justify your answer

Answer 1

Answer:

No it cant.

Step-by-step explanation:

3 is a positive integer.

If q = -1 then 4q+2 = -2

If q = 0 then 4q+2 = 2

If q = 1 then 4q+2 = 6

4q+2 is a straight line and -1,0,1 are consecutive integers so there are no integer values of q  where 4q+2 is 3

Answer 2

Every positive integer cannot be of the form 4q+2 because

when  q=0 ,

n=2

when q=1 ,

n=4*1+2=6

when q=2 ,

n=4*2+2=10

We can notice that numbers which are even and are not divisible by 4 can 

be written of the form 4q+2.

So, we can conclude that numbers which are not divisible by 4 ( we need to write a number in form 4q+2 and when we divide number with 4 we get remainder as 2) and numbers which are not odd ( as odd numbers are of the form 4q+1) can be written of the form 4q+2.