View Full Version : absolute value inequality
nicole
11-05-2013, 05:20 AM
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
11-05-2013, 05:21 AM
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
11-05-2013, 05:22 AM
Thanks Brynlee!!
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