English statements into mathematical statements So I have this statement:
Some integers less than 100 which are divisible by 7
can be written as 3 plus a multiple of 4"
I'm not sure the correct why to write it but I have many ways and they all kind of seem the same to me.
$∃x∈Z:x<100,\,7y=x \land3+4z=x:y,z∈Z$
or something like :
$∃x∈Z, x<100\,\land 3+4z=x\,\land 7y=x:y,z∈Z$
Sorry I'm quite new to this and I'm really confused about these notations and I also I was wondering when to use commas and when not to use commas. Our lecturer said in a pure mathematical proof commas aren't  used but in our text book commas are used to state the conditions on the set. Thanks!

Exact syntax and notation can vary; you should ask your lecturer. Quite frankly, extra symbols should generally be avoided in favour of English words (obscuring a proof using symbols doesn't magically make it more rigorous). If we really have to use symbols though, here's my version:
$$
\exists x,y,z \in \mathbb Z ~~~\text{s.t.}~~~[(x < 100) \land (x = 7y = 3 + 4z)]
$$
