document.write( "Question 813288: Solution set of: x^2 < x\r
\n" ); document.write( "\n" ); document.write( "with explanation please \n" ); document.write( "
Algebra.Com's Answer #489595 by AlbertusK(3)\"\" \"About 
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Have you already learnt about inequality? \r
\n" ); document.write( "\n" ); document.write( "If you're still a bit confuse about this case, I will try to give some helps.\r
\n" ); document.write( "\n" ); document.write( "Solution set of : x^2 < x...\r
\n" ); document.write( "\n" ); document.write( "We can change it into x^2 - x < 0\r
\n" ); document.write( "\n" ); document.write( "Now we factorize them : x(x - 1) < 0\r
\n" ); document.write( "\n" ); document.write( "Now we should find the zero-maker. In the last calculation, we already get
\n" ); document.write( "x(x-10) = 0. What are the roots for this equality?
\n" ); document.write( "The roots are x = 0 and (x-10)=0 --> x=10.
\n" ); document.write( "Now we have 2 roots namely 0 and 10. CLEAR?\r
\n" ); document.write( "\n" ); document.write( "Now let's consider 3 cases namely :
\n" ); document.write( "1) All numbers less than 0,
\n" ); document.write( "2) All numbers between 0 and 10,
\n" ); document.write( "3) All numbers more than 10.\r
\n" ); document.write( "\n" ); document.write( "for case 1), we can try any numbers for example -1. If we substitute -1 into the first inequality from your question [x^2-x < 0], we get [1-(-1)<0] --> [2<0] and this is a contradiction. \r
\n" ); document.write( "\n" ); document.write( "For case 2) we can try 2. we substitute 2 and we get a contradiction again.\r
\n" ); document.write( "\n" ); document.write( "For case 3) we can try 12. we substitute 12 and we get a contradiction again.\r
\n" ); document.write( "\n" ); document.write( "So the solution set for this problem is none. (no appropriate solution set --> empty solution). \n" ); document.write( "
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