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Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?
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08 Jul 2019, 03:59
5
3
we have 4 ranges to examine: at (\(x≥11\)) ,---------> \(x-3+x-5<x-11\) --> (\(x<-3\)) --------------> no common valid values at (\(11>x≥5\)) ,--> \(x-3+x-5<11-x\) --> (\(x<6.33\)) ------------> 5,6 are common at (\(5>x≥3\)) ,----> \(x-3+5-x<11-x\) --> (\(x<9\)) ----------------> 3,4 are common at (\(3>x\)) ,----------> \(3-x+5-x<11-x\) --> (\(x>-3\)) --------------> -2,-1,0,1,2 are common
Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?
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28 Oct 2019, 06:41
The thing is to understand that |x-3| means: The distance between x and 3. So the given inequality states that the combined distance between x and 3 plus distance between x and 5 is less than distance between x and 11. We can use the number line to easily count that there are 9 such x: -2,-1,0,1,2,3,4,5,6.
Does it help?
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gmatclubot
Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?
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28 Oct 2019, 06:41
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38% (02:37) correct 
