Sorry to open a new thread for an already existing question. was not satisfied with the answers.another-absolute-value-question-41274.html
If x is an integer, is x|x| < 2^x?
I can understand the second part:
-10|-10| < 2^-10 --> -10 * 10
< 1/2 ^ 10
|-10| --> reduced to 10 as its numeric.. is my reasoning correct?
B is sufficient
For (1) .. however i am not able to decipher anything..
-x|-x| < 2^-x --> -x * -x
< 1/2 ^x
|-x| --> reduced to -x as x < 0 .. is my reasoning correct?
But what should be the next steps .. Please help
Question: is \(x|x| < 2^x\)? Notice that the right hand side (RHS), \(2^x\), is always positive for any value of \(x\).
(1) \(x<0\) --> \(LHS=x*|x|=negative*positive=negative\) --> \((LHS=negative)<(RHS=positive)\). Sufficient.
(2) \(x=-10\) --> LHS is negative --> \((LHS=negative)<(RHS=positive)\). Sufficient.
For \(x<0\), \(|x|=-x\) yes. So for (1) \(LHS=x*(-x)\), \(x\) is negative, \(-x\) is positive. So \(LHS=x*(-x)=negative*positive=negative\).