If you distribute a negative factor, should you flip the inequality symbol? And why be specific

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
mulitply - 1

-x>-x-2

false

-x<-x-2

true

that is why we flop the inequality symbole