Solve the following congruence for x (Modulo Question)

Question

I need help in a question that I'm having a hard time understanding... It is asking to determine the congruence for $x$ and expressing the answer in the range 0-1000:

$$ 200 . x = 13 \pmod{1001} $$

I'm not sure what to do... So far I have determined that the inverse of $ 200 \pmod{1001} $ is $ -5 $ but I'm not sure how to find a range of congruency for $x$...

Any help will be appreciated,

Thanks

Answer 1

Just multiply both sides by $-5$ and you'll get $$x \equiv -65 \pmod{1001} \equiv -65 + 1001\pmod{1001} \equiv 936\pmod{1001}$$