Question

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

Answer 1

`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`