document.write( "Question 309760: what is one possible value of x for which x < 2 < 1/x ? \n" ); document.write( "
Algebra.Com's Answer #221538 by Edwin McCravy(20060) $\"\"$ $\"About$
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what is one possible value of x for which x < 2 < 1/x ?
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document.write( " is a possible value for x because\r\n" );
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document.write( "Inverting and multiplying that last expression,\r\n" );
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document.write( "or\r\n" );
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document.write( "and that is true!\r\n" );
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document.write( "Other possible values of x would be ,,, etc. \r\n" );
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document.write( "How did I get that?\r\n" );
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document.write( "Greater than zero means \"positive\"\r\n" );
document.write( "Less than zero means \"negative\"\r\n" );
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document.write( "We try Case 1:    (which means x is a positive number)\r\n" );
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document.write( "We multiply through the right inequality by positive number x\r\n" );
document.write( "and the inequality sign does not reverse:\r\n" );
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document.write( "Since x is a positive number in this case, and the product\r\n" );
document.write( " is negative, and since a positive number must \r\n" );
document.write( "be multiplied by a negative number in order to get a negative \r\n" );
document.write( "number, then  must be a negative number, so\r\n" );
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document.write( "In order for a positive number to be both less than 2\r\n" );
document.write( "and also less than , it needs to be less\r\n" );
document.write( "than \r\n" );
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document.write( "So therefore:\r\n" );
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document.write( "We try Case 2:    (which means x is a negative number)\r\n" );
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document.write( "If we multiply the second inequality by x, which in this case is \r\n" );
document.write( "negative, we reverse the inequality symbols:\r\n" );
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document.write( "Since x is a negative number in this case, and the product\r\n" );
document.write( " is negative, and since a negative number must \r\n" );
document.write( "be multiplied by a positive number in order to get a negative \r\n" );
document.write( "number, then  must be a positive number. But then\r\n" );
document.write( " implies  with contradicts .\r\n" );
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document.write( "So Case 2 is impossible.\r\n" );
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document.write( "We try Case 3:  x = 0\r\n" );
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document.write( "This is impossible since  would not be defined.\r\n" );
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document.write( "Therefore only Case 1 is possible, so the solution is\r\n" );
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document.write( "and the solution set is \r\n" );
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document.write( "So x can be any positive value between 0 and , exclusive of\r\n" );
document.write( ".  x could be any fraction whose numerator is less than half \r\n" );
document.write( "its denominator.  Or x could be any decimal whose tenths digit is less \\r\n" );
document.write( "than 5, such as .437 or .33339, etc.\r\n" );
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document.write( "Edwin
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