Inequalities Advanced Strategy

[gmat.tony.2009]

Hi,

On page 191 (Guide 3, Fourth Edition) the explanation for question 11 says that since x < 0, 4/x < -1/3 evaluates to -12 < x. Can somebody explain the steps that were taken to reach the given answer?

Thanks.

[parthatayi]

Hi,

On page 191 (Guide 3, Fourth Edition) the explanation for question 11 says that since x < 0, 4/x < -1/3 evaluates to -12 < x. Can somebody explain the steps that were taken to reach the given answer?

Thanks.

4/x<-1/3
=4/x>1/3
=x<12
=x>-12

[gmat.tony.2009]

Hi,

On page 191 (Guide 3, Fourth Edition) the explanation for question 11 says that since x < 0, 4/x < -1/3 evaluates to -12 < x. Can somebody explain the steps that were taken to reach the given answer?

Thanks.

4/x<-1/3
=4/x>1/3
=x<12
=x>-12

Thanks for your reply. But to solve this you assumed x to be +ve. Is this the correct approach? I am not doubting your approach...just need to clear it in my head.

[parthatayi]

Can you please post the complete question.

[gmat.tony.2009]

Can you please post the complete question.

If 4/x < -1/3, what are the possible range of values for x?

[parthatayi]

We need not worry abt the sign of x in this question.We shall treat x as positive.
We shall be careful if the question had included a modulus.
had it been 4/|x|,then we would have considered two conditions.
one is when x>0 and the another is x<0.

[adhirajkohli]

We need not worry abt the sign of x in this question.We shall treat x as positive.
We shall be careful if the question had included a modulus.
had it been 4/|x|,then we would have considered two conditions.
one is when x>0 and the another is x<0.

I don't think so, because if you assume x = 2 then that would mean:
4/2 < -1/3
i.e. 2 < -1/3 which is incorrect.
It is mentioned in the question that x < 0.
Therefore,
4/x < -1/3
*** Multiplying both sides by 'x' which is Negitive. ***
When we multiply or divide an inequality by a negitive quantity the SIGN changes.
4 > - x/3
*** Multiplying both sides by 3 ***
12 > -x
*** Multiplying both sides by -1 ***
-12 < x
This is what the explanation in the guide says.

[parthatayi]

We need not worry abt the sign of x in this question.We shall treat x as positive.
We shall be careful if the question had included a modulus.
had it been 4/|x|,then we would have considered two conditions.
one is when x>0 and the another is x<0.

I don't think so, because if you assume x = 2 then that would mean:
4/2 < -1/3
i.e. 2 < -1/3 which is incorrect.
It is mentioned in the question that x < 0.
Therefore,
4/x < -1/3
*** Multiplying both sides by 'x' which is Negitive. ***
When we multiply or divide an inequality by a negitive quantity the SIGN changes.
4 > - x/3
*** Multiplying both sides by 3 ***
12 > -x
*** Multiplying both sides by -1 ***
-12 < x
This is what the explanation in the guide says.

The main reason I have requested for the question is to check the condition on x.Please find the question in one of the posts above.It did not mention the condition for x.

[gmat.tony.2009]

We need not worry abt the sign of x in this question.We shall treat x as positive.
We shall be careful if the question had included a modulus.
had it been 4/|x|,then we would have considered two conditions.
one is when x>0 and the another is x<0.

I don't think so, because if you assume x = 2 then that would mean:
4/2 < -1/3
i.e. 2 < -1/3 which is incorrect.
It is mentioned in the question that x < 0.
Therefore,
4/x < -1/3
*** Multiplying both sides by 'x' which is Negitive. ***
When we multiply or divide an inequality by a negitive quantity the SIGN changes.
4 > - x/3
*** Multiplying both sides by 3 ***
12 > -x
*** Multiplying both sides by -1 ***
-12 < x
This is what the explanation in the guide says.

This makes sense. Thanks

[tim]

adhirajkohli, that is totally correct. The initial explanation by parthatayi had several mistakes, so please ignore that explanation in its entirety..