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

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Answer 1 · 2017-10-18T04:44:18

#x<-14 or x>22#

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#