document.write( "Question 365114: solve (x+3)(x-16)(x+2)>0 The solution set is {x ⎹ } \n" ); document.write( "

Algebra.Com's Answer #260345 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Break up the number line into 4 regions using the critical points of the function.
\n" ); document.write( "Region 1:( $\"-infinity\"$ , $\"-3\"$ )
\n" ); document.write( "Region 2:( $\"-3\"$ , $\"-2\"$ )
\n" ); document.write( "Region 3:( $\"-2\"$ , $\"16\"$ )
\n" ); document.write( "Region 4:( $\"16\"$ , $\"infinity\"$ )
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "For each region, choose a point in the region (not an endpoint).
\n" ); document.write( "Test the inequality.
\n" ); document.write( "If the inequality is satisfied, the region is part of the solution region.
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "Region 1: $\"x=-4\"$
\n" ); document.write( " $\"%28x%2B3%29%28x-16%29%28x%2B2%29%3E0\"$
\n" ); document.write( " $\"%28-4%2B3%29%28-4-16%29%28-4%2B2%29%3E0\"$
\n" ); document.write( " $\"%28-1%29%28-20%29%28-2%29%3E0+\"$
\n" ); document.write( " $\"-40%3E0+\"$
\n" ); document.write( "False, Region 1 is not part of the solution region.
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "Region 2: $\"x=-5%2F2\"$
\n" ); document.write( " $\"%28x%2B3%29%28x-16%29%28x%2B2%29%3E0\"$
\n" ); document.write( " $\"%28-5%2F2%2B3%29%28-5%2F2-16%29%28-5%2F2%2B2%29%3E0\"$
\n" ); document.write( " $\"%281%29%28-37%2F2%29%28-1%2F2%29%3E0+\"$
\n" ); document.write( " $\"37%2F4%3E0+\"$
\n" ); document.write( "True, Region 2 is part of the solution region.
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "Region 3: $\"x=0\"$
\n" ); document.write( " $\"%28x%2B3%29%28x-16%29%28x%2B2%29%3E0\"$
\n" ); document.write( " $\"%28-4%2B3%29%28-4-16%29%28-4%2B2%29%3E0\"$
\n" ); document.write( " $\"%283%29%28-16%29%282%29%3E0+\"$
\n" ); document.write( " $\"-96%3E0+\"$
\n" ); document.write( "False, Region 3 is not part of the solution region.
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "Region 4: $\"x=17\"$
\n" ); document.write( " $\"%28x%2B3%29%28x-16%29%28x%2B2%29%3E0\"$
\n" ); document.write( " $\"%2817%2B3%29%2817-16%29%2817%2B2%29%3E0\"$
\n" ); document.write( " $\"%2820%29%281%29%2819%29%3E0+\"$
\n" ); document.write( " $\"380%3E0+\"$
\n" ); document.write( "True, Region 4 is part of the solution region.
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "Solution Region:( $\"-3\"$ , $\"-2\"$ ) U ( $\"16\"$ , $\"infinity\"$ )
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "Graphical verification: Look for regions where the function is above the x-axis ( $\"y%3E0\"$ )
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );