How do I solve for negative modular arithmetic?

Question

Here is an example: -45 mod 13 = 7, but how?

Answer 1

-52 mod 13 = 0
-45-(-52)=7

Answer 2

You can add multiples of 13 until you get a positive number, example:
-45+4(13)=-45+52=7
or even
-45+10(13)=-45+130=85≡7 mod 13

Answer 3

Thanks for your help!

Also, I am kind of confused about finding the value of x.

Example: 9x ≡ 1 mod 10

How do I solve this?

Answer 4

how long will it take for a 10,000 investment to grow to 15,000if it is compounded continuously at 5 %