Disequazione con valore assoluto $|x+4|>5$

Text

Solve the inequality $|x+4|>5.$

Solution

An inequality of the form $|A|>k$ (with $k>0$) is equivalent to $A<-k\ \vee\ A>k$: $x+4<-5\ \vee\ x+4>5\implies x<-9\ \vee\ x>1.$ $\boxed{x<-9\ \vee\ x>1.}$