Question

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

Answer 1

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

Answer 2

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<-1 or x>7}