document.write( "Question 846031: Solve: (x+16)/(x-2)<=7 \n" ); document.write( "

Algebra.Com's Answer #509576 by Fombitz(32388) $\"\"$ $\"About$

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Subtract 7 from both sides.
\n" ); document.write( " $\"%28x%2B16%29%2F%28x-2%29-7%28%28x-2%29%2F%28x-2%29%29%3C=0\"$
\n" ); document.write( " $\"%28x%2B16-7x%2B14%29%2F%28x-2%29%3C=0\"$
\n" ); document.write( " $\"%28-6x%2B30%29%2F%28x-2%29%3C=0\"$
\n" ); document.write( "Look at the zeros of the numerator and the undefined values of the denominator and break up the number line.
\n" ); document.write( " $\"x=5\"$
\n" ); document.write( " $\"x=2\"$
\n" ); document.write( "Test for values less than 2, between 2 and 5, and greater than 5.
\n" ); document.write( "First, less than 2, $\"x=0\"$ , $\"30%2F%28-2%29%3C=0\"$ , $\"-15%3C=0\"$ , True.
\n" ); document.write( "Between 2 and 5, $\"x=3\"$ , $\"%28-18%2B30%29%2F%283-2%29%3C=0\"$ , $\"12%3C=0\"$ , False.
\n" ); document.write( "Greater than or equal to 5, $\"x=6\"$ , $\"%28-6%286%29%2B30%29%2F%286-2%29%3C=0\"$ , $\"-6%2F3%3C=0\"$ , $\"-2%3C=0\"$ , True.
\n" ); document.write( "So the solution set is,
\n" ); document.write( "( $\"-infinity\"$ , $\"2\"$ )U[ $\"5\"$ , $\"infinity\"$ )
\n" ); document.write( " \n" ); document.write( "

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