document.write( "Question 1052677: Solve the inequality and graph the solution set on a number line. Be sure to use closed dots or open circles. Do not use parentheses or brackets. \r
\n" ); document.write( "\n" ); document.write( "(x+4)/(x-3)<=0
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Algebra.Com's Answer #668008 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Choose the critical points from the left hand side.
\n" ); document.write( " $\"x=-4\"$ and $\"x=3\"$
\n" ); document.write( "Breakj up the number line into 3 regions:
\n" ); document.write( "R1: $\"x%3C-4\"$
\n" ); document.write( "R2: $\"-4%3Cx%3C3\"$
\n" ); document.write( "R3: $\"x%3E3\"$
\n" ); document.write( "For each region, choose a point in the region (not an endpoint),
\n" ); document.write( "Test the inequality in the region.
\n" ); document.write( "R1: $\"x=-5\"$
\n" ); document.write( " $\"%28-5%2B4%29%28-5-3%29%3C=0\"$
\n" ); document.write( " $\"%28-1%29%28-8%29%3C=0\"$
\n" ); document.write( " $\"8%3C=0\"$
\n" ); document.write( "False, R1 is not part of the solution.
\n" ); document.write( "R2: $\"x=0\"$
\n" ); document.write( " $\"%280%2B4%29%280-3%29%3C=0\"$
\n" ); document.write( " $\"%284%29%28-3%29%3C=0\"$
\n" ); document.write( " $\"-12%3C=0\"$
\n" ); document.write( "True, R2 is part of the solution.
\n" ); document.write( "R3: $\"x=4\"$
\n" ); document.write( " $\"%284%2B4%29%284-3%29%3C=0\"$
\n" ); document.write( " $\"%288%29%281%29%3C=0\"$
\n" ); document.write( " $\"8%3C=0\"$
\n" ); document.write( "False, R3 is not part of the solution.
\n" ); document.write( "So then the solution is,
\n" ); document.write( "[ $\"-4\"$ , $\"3\"$ )
\n" ); document.write( "You cannot include $\"x=3\"$ in the solution since the function is not defined at that point.
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