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m990540
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How to simplify? 09 Mar 2011, 08:56
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Hello,

Other than plugging in numbers, how could you simplify this equation?

1/X > -1

Thanks so much!



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How to simplify? 09 Mar 2011, 09:04
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m990540
Hello,

Other than plugging in numbers, how could you simplify this equation?

1/X > -1

Thanks so much!
Show more

\(\frac{1}{x}>-1\) (note you can not cross-multiply and write \(1>-x\) as you don't know the siign of \(x\)) --> \(\frac{1}{x}+1>0\) --> \(\frac{1+x}{x}>0\) --> \(x<-1\) or \(x>0\).

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

DS questions to practice: search.php?search_id=tag&tag_id=184
PS questions to practice: search.php?search_id=tag&tag_id=189

Hope it helps.
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How to simplify? 09 Mar 2011, 09:57
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Thanks Bunuel for the great explanation. Kudos given!
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How to simplify? 09 Mar 2011, 21:10
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i got x>0 or x<-1 too.

But what if we do a cross multiplication then wont we getting 1 > -x => -x<1 => x > -1

so if we compare second line solution with the first line solution how can x>-1 and x<-1 at the same time?Shouldnt we be getting same solution no matter how you do it?

what am i missing?

Bunuel
m990540
Hello,

Other than plugging in numbers, how could you simplify this equation?

1/X > -1

Thanks so much!

\(\frac{1}{x}>-1\) (note you can not cross-multiply and write \(1>-x\) as you don't know the siign of \(x\)) --> \(\frac{1}{x}+1>0\) --> \(\frac{1+x}{x}>0\) --> \(x<-1\) or \(x>0\).

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

DS questions to practice: search.php?search_id=tag&tag_id=184
PS questions to practice: search.php?search_id=tag&tag_id=189

Hope it helps.
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How to simplify? 10 Mar 2011, 04:24
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Spidy001
i got x>0 or x -x => -x x > -1
[/color]
so if we compare second line solution with the first line solution how can x>-1 and x -1

Thanks so much!
Show more

\(\frac{1}{x}>-1\) (note you can not cross-multiply and write \(1>-x\) as you don't know the siign of \(x\)) --> \(\frac{1}{x}+1>0\) --> \(\frac{1+x}{x}>0\) --> \(x0\).

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

DS questions to practice: search.php?search_id=tag&tag_id=184
PS questions to practice: search.php?search_id=tag&tag_id=189

Hope it helps.[/quote][/quote]

You should read the solution you quote carefully: "note you can not cross-multiply and write \(1>-x\) as you don't know the siign of \(x\)".

Never multiply or divide inequality by a variable (or by an expression with variable) unless you are sure of its sign since you do not know whether you must flip the sign of the inequality.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!