document.write( "Question 1152387: Hi! I had this interval: $\"+1.99%3C1%2Fx%3C2.01+\"$ . When I took the reciprocal of each number, I ended up with: $\"+1%2F1.99%3Cx%3C1%2F2.01+\"$ . However, this leaves me with the larger number on the left side and the smaller number on the right side. This wouldn't make sense. What did I do wrong? Can I rearrange the numbers?
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Algebra.Com's Answer #774396 by ikleyn(52799) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "The original compound inequality\r\n" );
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document.write( "    1.99 <  < 2.01\r\n" );
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document.write( "is (or represents) the system of two inequalities\r\n" );
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document.write( "    1.99 <      (1)\r\n" );
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document.write( "and\r\n" );
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document.write( "     < 2.01.    (2)\r\n" );
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document.write( "In particular, from the compound inequalities (1) and (2),  it follows that  is positive; hence x is positive.\r\n" );
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document.write( "Therefore, you can multiply both sides of each inequalities (1) and (2) by x  without changing the direction\r\n" );
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document.write( "of each inequality.\r\n" );
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document.write( "Doing it with the inequality (1), you get\r\n" );
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document.write( "    1.99x < 1;  hence,  x <  = 0.502513.    (3)\r\n" );
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document.write( "Doing it with the inequality (2), you get\r\n" );
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document.write( "    1 < 2.01x;  hence,  x >  = 0.497512.    (4)\r\n" );
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document.write( "From inequalities (3) and (4), you get the FINAL ANSWER\r\n" );
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document.write( "   0.497512 < x < 0.502513.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "It is how to solve and to analyze the given compound inequality accurately.\r
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\n" ); document.write( "\n" ); document.write( "If you are passionate about learning on how to solve such inequalities, look into my lessons\r
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\n" ); document.write( "\n" ); document.write( "Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.\r
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\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
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\n" ); document.write( "\n" ); document.write( "Come again to the forum soon to learn something new (!)\r
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