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If |x| > 3, which of the following must be true?
I. x > 3
II. x^2 > 9
I and II only
II and III only
I, II, and III
Option D is the correct answer.
Given, |x| > 3, which means either x>3 or x<-3
Now check the statements
I. x > 3 – not always true as x can be smaller than -3.Thus option A,C & E is ruled out. Only B & D are left.
II. X^2 > 9 – Always true for x>3 or x<-3 .To check – if x = 4,5,6,7…. or -4,-5,-6,-7, x^2>9
III. |x-1|>2, which means (x-1)>2 —> x>3 (if x-1>0) – True it also means (x-1)<-2—- >x<-1
(if x-1<0) X<-1 satisfies x<-3.
Thus true Both II and III, is true