Algebra.Com's Answer #735766 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "First, the formula is ambiguous, since it can be read in different ways.\r
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document.write( "One way to read it is f(x) =  .\r
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document.write( "Another way is f(x) =  .\r
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document.write( "To make it UNAMBIGOUS, you must use parentheses, showing which part is the numerator, and which is the denominator.\r
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document.write( "I will read the formula f(x) = .\r
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document.write( "The critical points are x=  (the zero of the numerator and the zero of the function),\r\n" );
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document.write( " x= 2 and x= 4 (the zeroes of the denominator).\r\n" );
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document.write( "They divide the number line in four intervals \r\n" );
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document.write( "  < x < , < x < 2, 2 < x < 4 and 4 < x <  .\r\n" );
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document.write( "1. In the interval < x < all three factors (2x-3), (x-2) and (x-4) are negative. \r\n" );
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document.write( " So, the function f(x) is negative as the product/quotient of three negative numbers.\r\n" );
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document.write( " So, this interval < x < is the part of the solution domain.\r\n" );
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document.write( "2. In the interval < x < 2, the factor (2x-3) is positive, while (x-2) and (x-4) are negative. \r\n" );
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document.write( " So, the function f(x) is positive as the product/quotient of one positive and two negative numbers.\r\n" );
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document.write( " So, this interval < x < 2, is not the part of the solution domain.\r\n" );
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document.write( "3. In the interval 2 < x < 4, the factors (2x-3) and (x-2) are positive, while (x-4) is negative. \r\n" );
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document.write( " So, the function f(x) is negative as the product/quotient of two positive and one negative numbers.\r\n" );
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document.write( " So, this interval 2 < x < 4, is the part of the solution domain.\r\n" );
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document.write( "4. In the interval 4 < x, the factors (2x-3), (x-2) and (x-4) are positive. \r\n" );
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document.write( " So, the function f(x) is positive as the product/quotient of three positive numbers.\r\n" );
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document.write( " So, this interval 4 < x is not a part of the solution domain.\r\n" );
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document.write( "Answer. The solution set is the union of two intervals (,) U (2,4).\r\n" );
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document.write( "Solved.\r
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document.write( "==================\r
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document.write( "To see many other similar solved problems, look into the lessons\r
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document.write( " - Solving problems on quadratic inequalities,\r
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document.write( " - Solving inequalities for high degree polynomials factored into a product of linear binomials \r
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document.write( " - Solving inequalities for rational functions with numerator and denominator factored into a product of linear binomials \r
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document.write( "in this site.\r
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