Number Theory and Congruency I have the following problem:
$$2x+7=3 \pmod{17}$$
I know HOW to do this problem. It's as follows:
$$2x=3-7\\
x=-2\equiv 15\pmod{17}$$
But I have no idea WHY I'm doing that. I don't really even understand what the problem is asking, I'm just doing what the book says to do. Can someone explain what this problem is asking and what I'm finding? Thanks

The first two lines are solving a linear equation as you are used to.  I suspect the problem is the conversion $-2 \equiv 15 \pmod {17}$  In modular arithmetic we regard numbers that differ by the modulus as equivalent.  If you plug you solution in, you get $2\cdot 15 +7=37$  Now we subtract off all the multiples of $17$ we can and get $2 \cdot 15+7=37 \equiv 3 \pmod {17}$
