If |x - 3| > 1 then which of the following must be true?
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Updated on: 04 Jul 2019, 21:56
If |x−3|>1 then which of the following must be true?
I. |x|>4
II. x^2>16
III. x>4
Given that |x−3|>1, it follows that x<2 or x>4. Possible values of x include 0,1,5,...
I. |x|>4
Given that |x|>4, it follows that x<-4 or x>4.
For every value that |x−3|>1 can take (e.g. x=0,1,5), must it be true that x<-4 or x>4 ? Nope.
Although x=5 fits well within |x|>4, both x=0 and x=1 never do.
Statement I is not necessarily true
II. x^2>16
Given that x^2>16, it follows that (x-4)(x+4)>0 and then x<-4 or x>4.
For every value that |x−3|>1 can take (e.g. x=0,1,5), must it be true that x<-4 or x>4 ? Nope.
Although x=5 fits well within x^2>16, both x=0 and x=1 never do.
Statement II is not necessarily true
III. x>4
For every value that |x−3|>1 can take (e.g. x=0,1,5), must it be true that x>4 ? Obviously not. Both x=0 and x=1 never satisfy x>4.
Statement III is not necessarily true
Answer is (E) None.
Originally posted by
freedom128 on 04 Jul 2019, 21:52.
Last edited by
freedom128 on 04 Jul 2019, 21:56, edited 1 time in total.