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Inequality

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by DCJ » Sun Jul 26, 2009 10:20 pm
Double-checking since I saw what seems to be a mistake in a text

(-1/x)>17

Does the above equation simplify to
x<(-1/17) or x>(-1/17)
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by ankitns » Wed Jul 29, 2009 7:00 pm
X < -1/17

Cheers.
Attempt 1: 710, 92% (Q 42, 63%; V 44, 97%)
Attempt 2: Coming soon!
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by gmat_2010 » Thu Jul 30, 2009 3:20 am
It will be X > -17

The inequality sign changes twice. Once for inversion of 1/x to x. One for changing -X to X. Hence, the sign remains the same in the final answer.

(-1/x)>17
Therefore, -x < 1/17
Therefore, x > -1/17

Check:
Assume x = -1/18 which is greater than -1/17

(-1/x) = 18 which is greater than 17.
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by DCJ » Thu Jul 30, 2009 9:17 am
X < -1/17 is the correct answer. -1/18<-1/17
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by Ian Stewart » Thu Jul 30, 2009 12:41 pm
DCJ wrote:X < -1/17 is the correct answer. -1/18<-1/17
-1/18 is greater than -1/17, since it is closer to zero on the number line.

In this inequality:

-1/x > 17

x must be negative, since the value of -1/x is positive (it's greater than 17). So when we multiply by x on both sides, we're multiplying by a negative, and we need to reverse the inequality:

-1/x > 17
-1 < 17x
-1/17 < x

and since we know x is negative, we know that -1/17 < x < 0.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by srisanj4 » Mon Aug 03, 2009 11:29 pm
Agreed. x>-1/17
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