document.write( "Question 69638: solve: $\"2x%28x-1%29%3C+-3%282-2x%29\"$ \n" ); document.write( "

Algebra.Com's Answer #49737 by stanbon(75887) $\"\"$ $\"About$

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2x(x-1)< -3(2-2x)
\n" ); document.write( "2x^2-2x < -6+6x
\n" ); document.write( "2x^2-8x+6<0
\n" ); document.write( "x^2-4x+3<0
\n" ); document.write( "(x-3)(x-1)<0
\n" ); document.write( "Mark 1 and 3 on a number line ; this determines 3 intervals.
\n" ); document.write( "Check a test point in each interval to see where the solution set lies:
\n" ); document.write( "Check x=0 in interval (-inf,1);(0-3)(0-1)<0; no, so no solution in (-inf,1)
\n" ); document.write( "Check x=2 in interval (1,3);(2-3)(2-1)<0; yes, that interval part of solution
\n" ); document.write( "Check x=10 in interval (3,inf); (10-3)(10-1)<0: no, so no solution in (3,inf)
\n" ); document.write( "----------
\n" ); document.write( "Conclusion: The solution set is the interval (1,3)\r
\n" ); document.write( "\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( " \n" ); document.write( "

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