Find all the values of x such that abs(7-abs(4-x))>11?

1 Answer
Oct 18, 2017

x<-14 or x>22

Explanation:

Since |f(x)|>a is solved by the equivalent inequalities:

f(x)<-a or f(x)>a, we get, in the first step:

7-|4-x|<-11 or 7-|4-x|>11

Then we would reduce to get:

|4-x|>18 or color(red)(|4-x|<-4)

The second inequality is false, then:

(4-x<-18 or 4-x>18)

that's

x>22 or x<-14