very basic algebra

I was told long ago way back when that when you have something like this -x = 7 you solve for x by doing the following (-x = 7)- x = -7 but now that I think about it your not actually multiplying by negative one what is actually happening is this right???...

my teachers use to tell me that you could just multiply by negative one because it dosen't change its value but that is not true as it changes its direction