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Guys, I do understand how to do it through plugging in numbers, can someone elaborate the method, where you use algebraic method. It would be great help! Thank you, I am considering two options x>0 and x<0 1) x>0 then cross multiplying we get x<x^2 then we find out that x is >1

2) x<0 then cross multiplying we get that x>-x^2 then we get that x is between -1 and 0 thus, x is between -1 and 0 and x>1

Guys, I do understand how to do it through plugging in numbers, can someone elaborate the method, where you use algebraic method. It would be great help! Thank you, I am considering two options x>0 and x<0 1) x>0 then cross multiplying we get x<x^2 then we find out that x is >1

2) x<0 then cross multiplying we get that x>-x^2 then we get that x is between -1 and 0 thus, x is between -1 and 0 and x>1

If \frac{x}{|x|} \lt x , which of the following must be true about x? (x \ne 0) A. x\gt 2 B. x \in (-1,0) \cup (1,\infty) C. |x| \lt 1 D. |x| = 1 E. |x|^2 \gt 1

Absolute value properties: Absolute value is always non-negative: |x|\geq{0} (not positive but non-negative, meaning that absolute value can equal to zero), so: When x\leq{0} then |x|=-x (note that in this case |x|=-negative=positive); When x\geq{0} then |x|=x.

B. Substitute numbers. I chose 3, -3, -1/3 & 1/3 for 3 & -1/3 the inequality holds good. Instead of 3 we can have any number between 1 & infinity. Similarly instead of -1/3 we can have any number between 0 & -1

Hi all, i disagree with most of you. My Answer is A. Explanation:- x/|x| <x Case 1: if x<0 If x<0, say a no -3. Then, -3/|-3|<-3 -3/3<-3 -1<-3 which is not true. Case 2: x=0 Not applicable, as per the given condition. Case 3: if x>0 Take a no say 1(x>0) Then, 1/|1|<1 1/1<1 1<1 which is not true. Take another no say 2(x>0) Then, 2/|2|<2 2/2<2 1<2 which is true. So , for a Question like which of the following must be true about ? ( )

The answer is X>2, which is Option A. _________________

kudos me if you like my post.

Attitude determine everything. all the best and God bless you.

Hi Dauren, Here is my solution. My ANS is A. Explanation:- x/|x| <x Case 1: if x<0 If x<0, say a no -3. Then, -3/|-3|<-3 -3/3<-3 -1<-3 which is not true. Case 2: x=0 Not applicable, as per the given condition. Case 3: if x>0 Take a no say 1(x>0) Then, 1/|1|<1 1/1<1 1<1 which is not true. Take another no say 2(x>0) Then, 2/|2|<2 2/2<2 1<2 which is true. So , for a Question like which of the following must be true about ?

The answer is X>2, which is Option A.

!!!Give me Kudos if you like my post.!!!! _________________

kudos me if you like my post.

Attitude determine everything. all the best and God bless you.

Hi all, i disagree with most of you. My Answer is A. Explanation:- x/|x| <x Case 1: if x<0 If x<0, say a no -3. Then, -3/|-3|<-3 -3/3<-3 -1<-3 which is not true. Case 2: x=0 Not applicable, as per the given condition. Case 3: if x>0 Take a no say 1(x>0) Then, 1/|1|<1 1/1<1 1<1 which is not true. Take another no say 2(x>0) Then, 2/|2|<2 2/2<2 1<2 which is true. So , for a Question like which of the following must be true about ? ( )

The answer is X>2, which is Option A.

Number plugging is not the best method to solve this question.

OA for this question is B, not A: the given inequality holds true in two ranges -1<x<0 and x>1 (see solution in my previous post). You can try values from this ranges to check. So x>2 is not always true. _________________

Hi all, i disagree with most of you. My Answer is A. Explanation:- x/|x| <x Case 1: if x<0 If x<0, say a no -3. Then, -3/|-3|<-3 -3/3<-3 -1<-3 which is not true. Case 2: x=0 Not applicable, as per the given condition. Case 3: if x>0 Take a no say 1(x>0) Then, 1/|1|<1 1/1<1 1<1 which is not true. Take another no say 2(x>0) Then, 2/|2|<2 2/2<2 1<2 which is true. So , for a Question like which of the following must be true about ? ( )

The answer is X>2, which is Option A.

Number plugging is not the best method to solve this question.

OA for this question is B, not A: the given inequality holds true in two ranges -1<x<0 and x>1 (see solution in my previous post). You can try values from this ranges to check. So x>2 is not always true.

x>2 will alwayz be true as it is a part of (-1,0)& (1,infinity) anyway, i realized my mistake. the answer will be B. thnx buddy! _________________

kudos me if you like my post.

Attitude determine everything. all the best and God bless you.

Hi all, i disagree with most of you. My Answer is A. Explanation:- x/|x| <x Case 1: if x<0 If x<0, say a no -3. Then, -3/|-3|<-3 -3/3<-3 -1<-3 which is not true. Case 2: x=0 Not applicable, as per the given condition. Case 3: if x>0 Take a no say 1(x>0) Then, 1/|1|<1 1/1<1 1<1 which is not true. Take another no say 2(x>0) Then, 2/|2|<2 2/2<2 1<2 which is true. So , for a Question like which of the following must be true about ? ( )

The answer is X>2, which is Option A.

Number plugging is not the best method to solve this question.

OA for this question is B, not A: the given inequality holds true in two ranges -1<x<0 and x>1 (see solution in my previous post). You can try values from this ranges to check. So x>2 is not always true.

x>2 will alwayz be true as it is a part of (-1,0)& (1,infinity) anyway, i realized my mistake. the answer will be B. thnx buddy!

No, that's not correct.

Given inequality holds true for -1<x<0 and x>1, so if x is in the range -1<x<0 (for example if x=-0.5) or in the range 1<x\leq{2} (for example if x=1.5) then x>2 won't be true.

Very good question My attempt: given x/|x|<X and x is not equal to 0 option 1:if x > 2 let say x=3 then 3/3 = 1 which is < than 3 hence true. same can be stated about X= 2 hence must not be true.

option 2 : if -1<x<0 and 1<x<infinity. lets assume X is -0.5 then -1 < -.05 true. x=2 then 1< 2 true. this statement must be true for all values of X as per inequality given answer must be B _________________

If \frac{x}{|x|} \lt x , which of the following must be true about x? (x \ne 0) A. x\gt 2 B. x \in (-1,0) \cup (1,\infty) C. |x| \lt 1 D. |x| = 1 E. |x|^2 \gt 1

Absolute value properties: Absolute value is always non-negative: |x|\geq{0} (not positive but non-negative, meaning that absolute value can equal to zero), so: When x\leq{0} then |x|=-x (note that in this case |x|=-negative=positive); When x\geq{0} then |x|=x.

If \frac{x}{|x|} \lt x , which of the following must be true about x? (x \ne 0) A. x\gt 2 B. x \in (-1,0) \cup (1,\infty) C. |x| \lt 1 D. |x| = 1 E. |x|^2 \gt 1

Absolute value properties: Absolute value is always non-negative: |x|\geq{0} (not positive but non-negative, meaning that absolute value can equal to zero), so: When x\leq{0} then |x|=-x (note that in this case |x|=-negative=positive); When x\geq{0} then |x|=x.

Bunuel I got this question but the answer weren't the same as you have posted here. They had the original choices as posted in page 1. I got the correct solution but since the answer choices given were incorrect, I chose the wrong one.

Please do review this question on GC CATS. _________________

Bunuel I got this question but the answer weren't the same as you have posted here. They had the original choices as posted in page 1. I got the correct solution but since the answer choices given were incorrect, I chose the wrong one.