Absolute value inequality

  • #1
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Question:
True or False If x^2<4 then |x|<=2

My solution:
I get -2<x<2 when I solve the problem so it should be false. Yet the text says its true? Is this a mistake? If |x| is equal to 2 then it should be a closed interval, not an open interval which seems to be correct to me.
 
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  • #2
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Question:
True or False If x^2<4 then |x|<=2

My solution:
I get -2<x<2 when I solve the problem so it should be false. Yet the text says its true? Is this a mistake? If |x| is equal to 2 then it should be a closed interval, not an open interval which seems to be correct to me.
x2 < 4 is equivalent to -2 < x < 2 or |x| < 2. What the text has appears to be a typo.
 
  • #3
PeroK
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Question:
True or False If x^2<4 then |x|<=2

My solution:
I get -2<x<2 when I solve the problem so it should be false. Yet the text says its true? Is this a mistake? If |x| is equal to 2 then it should be a closed interval, not an open interval which seems to be correct to me.
It's probably a typo, although logically it is true:

If ##x^2 < 4## then ##|x| < 2## hence ##|x| \le 2##

If it were false, then there would be ##x## with ##|x| > 2## yet ##x^2 < 4##
 
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