Is |x-5| 4 given that x^2

Question

Is  |x-5| > 4  
given that 
 x^2 < 1  ?

Please explain your answer.

young_gun · Answer

i think the answer is NO. if i'm correct ill gladly explain.

elgo · Answer

I think, it's YES The Q asks "is|x-5|> 4". In other words, it asks whether (x-5)>4, which means that x>9, or -(x-5)>4, which means that x<1. x^2<1 says that x is between -1 and 1 (any squared number from this range is less than 1) So, the question is whether x<1orx>9 given that x>-1 AND x<1. And the answer is YES. Let's go another way. Pick numbers. X could be 0.5, so |0.5-5|=|-4.5|=4.5 is greater than 4. YES x=-0.5, then |-0.5-5|=|-5.5|=5.5 is also greater than 4. YES you can pick any number between -1 and 1 and the answer will be YES. PS I got some troubles while posting: system doesn't display correctly what I wrote:(

young_gun · Answer

"So, the question is whether x<1orx>9 given that x>-1 AND x<1. And the answer is YES. " why is it "or" in: x<1orx>9

elgo · Answer

Cuz, this inequality (|x-5| > 4) works only when absolute value of (x-5) is greater than 4. So, if x=9.5, it works. But if x=8.5, it doesn't, cuz |8.5-5|=3.5 which is not > 4, So, x must be >9. By the same token, x must be < 1. Let's take 1.5: |1.5-5|=|-3.5|=3.5 which is not > 4. But if you take 0.5, then |0.5-5|=|-4.5|=4.5 which IS > 4. That's why there is "OR".

bkk145 · Answer

Yes |x-5|>4 means x<1 and x>9 x^2 < 1 means -1

young_gun · Answer

what i don't understand is, how is x>9 if -1<x<1 ?

bkk145 · Answer

Is |x-5| > 4 given that x^2 4 means x9 x^2 9 if -14 is true? Since |x-5|>4 means x9, and given that -14 must be true because -1

Is |x-5| > 4 given that x^2 < 1

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