document.write( "Question 1179033: Given that p is a whole number, and 1/4 < 2/p < 1/3, what is the value of p? \n" ); document.write( "

Algebra.Com's Answer #808551 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Your starting inequality is\r\n" );
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document.write( "     <  < \r\n" );
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document.write( "It is so called \"compound inequality\", and it is equivalent to two separate inequalities\r\n" );
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document.write( "     <     (1)\r\n" );
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document.write( "and\r\n" );
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document.write( "     < ,   (2)\r\n" );
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document.write( "connected by the service word \"and\".\r\n" );
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document.write( "From inequality (1), multiplying both sides by positive number 4p, you get an EQUIVALENT inequality\r\n" );
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document.write( "    p < 4*2 = 8.    (3)\r\n" );
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document.write( "From inequality (2), multiplying both sides by positive number 3p, you get an EQUIVALENT inequality\r\n" );
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document.write( "    p > 3*2 = 6.    (4)\r\n" );
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document.write( "So, from (3) and (4) you have\r\n" );
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document.write( "    6 < p < 8.\r\n" );
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document.write( "There is only one integer number, satisfying this compound inequality :  p = 7.    ANSWER\r\n" );
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