2| x - 3 | > 8, 2| x - 3 | < - 8 Sovle the inequality involving absolute value? I don't understand how to get the right answer

Divide both sides by 2

|x-3|>4 and |x-3|<-4

ok so |x-3|<-4 is false, since |x|≥0 always

so we have

|x-3|>4

now assume

x-3>4 and

x-3<-4

x-3>

add 3

x>7

x-3<-4

add 3

x<-1

so

-1>x and x>7

so basically it is all numbers from - ∞ to + ∞ except from - 1 to 7

in interval notaion

(-∞,-1) U (7,∞)

S=x

X >7 and X > - 1 that would be the answer