absolute value inequality

[nicole]

Which of the following is true given that |x+4|<5?

(A) x<1

(B) -9<x<1

(C) x<-9 \ or \ x>1

(D) x<1 \ or \ x>-9

(E) 1<x<9


Thanks!:):)

[Brynlee]

Inequalities involving absolute values can be considered as either conjunctions or disjunctions.
For example the absolute value – inequality |x|<a / where / a>0 is equivalent to the conjunction -a<x<a . If a<0 then the aforementioned inequality has no solution.

While the absolute value – inequality |x|>a \ where \ a>0 is equivalent to the disjunction x<-a \ or\ x>a. If a<0 then the aforementioned inequality has infinite solutions.

In our case the inequality |x+4|<5 is a conjunction and can be solved as follows

|x+4|<5 \Rightarrow -5<x+4<5 \Rightarrow -9<x<1

Therefore the correct answer is (B).

[nicole]

Thanks Brynlee!!