document.write( "Question 329596: What is the solution set of y^2 - 2y ≤ 3y + 14?\r
\n" ); document.write( "\n" ); document.write( "(A) y ≥ -2
\n" ); document.write( "(B) y ≤ 7
\n" ); document.write( "(C) y ≤ -2 or y ≥ 7
\n" ); document.write( "(D) -7 ≤ y ≤ 2
\n" ); document.write( "(E) -2 ≤ y ≤ 7
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Algebra.Com's Answer #236276 by Fombitz(32388)\"\" \"About 
You can put this solution on YOUR website!
\"y%5E2-+2y+%3C=3y+%2B+14\"
\n" ); document.write( "\"y%5E2-+5y+-14%3C=0\"
\n" ); document.write( "\"%28y-7%29%28y%2B2%29%3C=0\"
\n" ); document.write( "Break up the number line into 3 regions.
\n" ); document.write( "Region 1:( \"-infinity\",\"-2\")
\n" ); document.write( "Region 2:(\"-2\",\"7\")
\n" ); document.write( "Region 3:(\"7\", \"infinity\")
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "Choose a point in the region and test the inequality.
\n" ); document.write( "Region 1: \"x=-3\"
\n" ); document.write( "\"%28-3-7%29%28-3%2B2%29%3C=0\"
\n" ); document.write( "\"%28-10%29%28-1%29%3C=0\"
\n" ); document.write( "\"10%3C=0\"
\n" ); document.write( "False, this region is not part of the solution.
\n" ); document.write( ".
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\n" ); document.write( "Region 2: \"x=0\"
\n" ); document.write( "\"%280-7%29%280%2B2%29%3C=0\"
\n" ); document.write( "\"%28-7%29%282%29%3C=0\"
\n" ); document.write( "\"-14%3C=0\"
\n" ); document.write( "True, this region is part of the solution.
\n" ); document.write( ".
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\n" ); document.write( "Region 3: \"x=8\"
\n" ); document.write( "\"%288-7%29%287%2B2%29%3C=0\"
\n" ); document.write( "\"%281%29%289%29%3C=0\"
\n" ); document.write( "\"9%3C=0\"
\n" ); document.write( "False, this region is not part of the solution.
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\n" ); document.write( ".
\n" ); document.write( "The solution region is Region 2.
\n" ); document.write( "E) is the correct answer.
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