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when x>0 we have 1/x < 1 and 1 < xsam2304 wrote:If x ≠ 0 and x/|x| < x, which of the following must be true ?
A.x > 1
B.x > −1
C.|x| < 1
D.|x| > 1
E.−1 < x < 0
For x > 0, |x| = x ---> x/|x| = x/x = 1sam2304 wrote:If x ≠ 0 and x/|x| < x, which of the following must be true ?
I am confused with the bold part. I tried to plot in graph for better understanding, yet I wasn't clear. How is it, x > -1 from both the statements ? Where am I going wrong ?Anurag@Gurome wrote:For x > 0, |x| = x ---> x/|x| = x/x = 1sam2304 wrote:If x ≠ 0 and x/|x| < x, which of the following must be true ?For x < 0, |x| = -x ---> x/|x| = x/(-x) = -1
- Now if |x|/x < x, then 1 < x
Therefore, either -1 < x < 0 or x > 1.
- Now if |x|/x < x, then -1 < x. Hence, -1 < x < 0
In both cases, x > -1
The correct answer is B.
Try to DISPROVE the answer choices.sam2304 wrote:If x ≠ 0 and x/|x| < x, which of the following must be true ?
A.x > 1
B.x > −1
C.|x| < 1
D.|x| > 1
E.−1 < x < 0
Because x > 1 means x is greater than -1. Also -1 < x < 0 means x greater than -1.sam2304 wrote:How is it, x > -1 from both the statements ?
These two points cleared my doubts. I was interpreting it the way you mentioned. Thanks a lot Anurag.Anurag@Gurome wrote: B. x > -1 ---> This is true about x for both the ranges.
Keep in mind that what the question have asked is not same as "For what range of values of x, x/|x| < x?"
What if x = 1? This does not fit into the statement! Could you please help me what am I missing?Anurag@Gurome wrote:Because x > 1 means x is greater than -1. Also -1 < x < 0 means x greater than -1.sam2304 wrote:How is it, x > -1 from both the statements ?
The question asked which of the following must be true for x. None of the options other than C, i.e. x > -1 is true about x. To make it more clear,Keep in mind that what the question have asked is not same as "For what range of values of x, x/|x| < x?"
- A. x > 1 ---> If -1 < x < 0, then this is not true about x.
B. x > -1 ---> This is true about x for both the ranges.
C. |x| < 1 ---> If x > 1, then this is not true about x.
D. |x| > 1 ---> If -1 < x < 0, then this is not true about x.
E. -1 < x < 0 ---> If x > 1, then this is not true about x.
Hope that helps.
You are thinking the same way I did. First we have to understand the question properly. Given x/|x| < x is true. Break down the inequality and find the range which comes for the given condition. Check the diagram which I have posted above. x > 1 and -1 < x < 0 are two intervals which are satisfied by the inequality x/|x| < x. What the question asks is to find the range which fits both these intervals or shaded region in the picture. Now look at the answer choices and you will find the answer easily.bubbliiiiiiii wrote: What if x = 1? This does not fit into the statement! Could you please help me what am I missing?
