OreoShake wrote:
Bunuel wrote:
Hussain15 wrote:
If x is not equal to 0, is |x| less than 1?
(1) x/|x|< x
(2) |x| > x
Will really appreciate if answer is supported by explanation.
(1) x/|x|< x
(2) |x| > x
Will really appreciate if answer is supported by explanation.
\(x\neq{0}\) , is\(|x|<1\) ? Which means is\(-1<x<1\) ?(\(x\neq{0}\) )
(1)\(\frac{x}{|x|}< x\)
Two cases:
A.\(x<0\) -->\(\frac{x}{-x}<x\) -->\(-1<x\) . But remember that\(x<0\) , so\(-1<x<0\)
B.\(x>0\) -->\(\frac{x}{x}<x\) -->\(1<x\) .
Two ranges\(-1<x<0\) or\(x>1\) . Which says that\(x\) either in the first range or in the second. Not sufficient to answer whether\( -1<x<1\)
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