document.write( "Question 354159: How do I solve the following inequality using interval notation? 1/x-3 <= 1/x-5 \n" ); document.write( "
Algebra.Com's Answer #253139 by stanbon(75887)\"\" \"About 
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How do I solve the following inequality using interval notation?
\n" ); document.write( "1/(x-3) <= 1/(x-5)
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\n" ); document.write( "x cannot be 3 and it cannot be 5.
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\n" ); document.write( "Solve the equality.
\n" ); document.write( "1/(x-3) = 1/(x-5)
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\n" ); document.write( "x-5 = x-3
\n" ); document.write( "No solution: So no solution for the equality part of the problem.
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\n" ); document.write( "Draw a number line and plot x = 3 and x = 5.
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\n" ); document.write( "Test values in the resulting intervals to find inequality solutions.
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\n" ); document.write( "1/(x-3)<1/(x-5)
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\n" ); document.write( "If x = 0 you get 1/-3 < 1/-5: true, so solution in (-inf,3)
\n" ); document.write( "If x = 4 you get 1/1 < 1/-1: false
\n" ); document.write( "If x = 10 you get 1/7 < 1/5: true, so solutions in (5,+inf)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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