document.write( "Question 1074120: I need help solving this rational inequality algebraically. 4/x+2 > 2 \n" ); document.write( "
Algebra.Com's Answer #688852 by Edwin McCravy(20062) $\"\"$ $\"About$
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "The tutor above points out something that I have long known.\r\n" );
document.write( "It is virtually impossible to successfully teach students to write\r\n" );
document.write( "mathematics containing fractions correctly all on one line.\r\n" );
document.write( "\r\n" );
document.write( "You wrote this:\r\n" );
document.write( "\r\n" );
document.write( "4/x+2 > 2\r\n" );
document.write( "\r\n" );
document.write( "which means this , which is the way the tutor took\r\n" );
document.write( "it. \r\n" );
document.write( "\r\n" );
document.write( "However I reason that since you are taking a higher level of\r\n" );
document.write( "algebra, your teacher would not be testing you to see if you are\r\n" );
document.write( "able to do a simple thing like the first step would require, to\r\n" );
document.write( "subtract 2 from both sides to get \r\n" );
document.write( "\r\n" );
document.write( "Therefore I assume that you meant this: \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "instead, which when written on one line would require parentheses\r\n" );
document.write( "around the denominator; otherwise the +2 will not be taken as part \r\n" );
document.write( "of the denominator but will be taken as a separate term.  So it \r\n" );
document.write( "should be written this way:\r\n" );
document.write( "\r\n" );
document.write( "4/(x+2) > 2 \r\n" );
document.write( "\r\n" );
document.write( "------------------------------\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We find the critical numbers by setting\r\n" );
document.write( "numerator = 0 and denominator = 0\r\n" );
document.write( "\r\n" );
document.write( "2x = 0;   x+2 = 0\r\n" );
document.write( " x = 0;     x = -2\r\n" );
document.write( "\r\n" );
document.write( "[Note: These critical numbers are NOT permissible values of x]\r\n" );
document.write( "\r\n" );
document.write( "We place the critical numbers on a number line:\r\n" );
document.write( "\r\n" );
document.write( "-------o-----o------------\r\n" );
document.write( "-4 -3 -2 -1  0  1  2  3  4\r\n" );
document.write( "\r\n" );
document.write( "We test a value for x left of -2, say -3 in this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That's false so we do not shade left of -2\r\n" );
document.write( "\r\n" );
document.write( "We test a value for x between -2 and 0, say -1 in this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That's true so we shade between -2 and 0.\r\n" );
document.write( "\r\n" );
document.write( "-------o=====o------------\r\n" );
document.write( "-4 -3 -2 -1  0  1  2  3  4\r\n" );
document.write( "\r\n" );
document.write( "We test a value for x right of 0, say 1 in this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This is false so we do not shade to the right of 0.\r\n" );
document.write( "\r\n" );
document.write( "Answer {x | -2 < x < 0} in set-builder notation \r\n" );
document.write( "       or (-2,0) in interval notation.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );