you flip is when you mulitply the whole equation by a negative not when you distribute a negative if yo had -3(x+4)>x you wouldn't flip the negative symbol when distributing then -3
but if you had -3(x+4)>-x you would eventually have to multiply by -1 to make +1x
because they will be differente exaple
12>3 is true if yo multiply negative -12>-3 is fale -12<-3 is true
anothe rexample with placeholders x<x+2 mulitply -1 -x>-x-2 false -x<-x-2 true that is why we flop the inequality symbole
