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

Determine every positive integer can be of the form $4q+2$, where $q$ is an integer.

All numbers of type $4q+2$ Where $\text{'}q\text{'}$is an integer, are even integers that are not divisible by $\text{'}4\text{'}$.
For Example,
When $q=1,$

$4q+2=4\left(1\right)+2=6$
When $q=2$,

$4q+2=4\left(2\right)+2=100$

When $q=0$,

$4q+2=4\left(0\right)+2=2$ and so on.

As a result, any integer of type $4q+2$returns only even values that are not multiples of $4$.

Hence, we can express odd numbers in this form.

Hence, every positive integer cannot be expressed in form $4q+2$.