danmac0710
  • danmac0710
Please help me solve: 2/(2x-5)<1/(x+7)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
be very very careful here
anonymous
  • anonymous
you do not know the sign of \(x\) so you cannot do the usual stuff like "cross multiply" or flip them you have to start with \[\frac{2}{2x-5}-\frac{1}{x+7}<0\] then solve
phi
  • phi
satellite showed you how to start. It is *always* safest to add or subtract when solving relations. once you get \[ \frac{2}{2x-5}-\frac{1}{x+7}<0 \] add the two fractions to get \[ \frac{ 2x+14-2x + 5}{(2x-5)(x+7)} < 0 \] the top simplifies to 19: \[ \frac{ 19}{(2x-5)(x+7)} < 0 \] now ask yourself: when is the left side negative ? (i.e. less than zero) it is negative if (2x-5) is positive and *at the same time* x+7 is negative (because + times - is -). so you need 2x-5 > 0 and x+7<0 or (2x-5) is negative and *at the same time* x+7 is positive 2x-5 < 0 and x+7> 0 can you finish ?

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danmac0710
  • danmac0710
Thank you ever so much. That is just what I needed!

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