document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=381601>Question 381601</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following solutions to the quadratic inequality\r<BR>\n" );
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document.write( "(x - 2)(x + 1) > 4\r<BR>\n" );
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document.write( "is correct? Explain why the others are incorrect.\r<BR>\n" );
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document.write( "a) Solution 1<BR>\n" );
document.write( "Since (x - 2)(x + 1) > 4 means that x - 2 > 4 or x + 1 > 4 ,we have the following:\r<BR>\n" );
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document.write( "if x - 2 > 4 , then x > 6 and if x + 1 > 4 , then x > 3.<BR>\n" );
document.write( "Therefore the solution to the inequality is the interval (3,&#8734;).\r<BR>\n" );
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document.write( "b) Solution 2<BR>\n" );
document.write( "Since (x - 2)(x + 1) > 4 means that (x - 2)(x + 1) - 4 > 0 , we have the following:\r<BR>\n" );
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document.write( "Either (x - 2)(x + 1) > 0 or -4 > 0 and since -4 is never greater than 0 we<BR>\n" );
document.write( "need only worry about (x - 2)(x + 1) > 0 .\r<BR>\n" );
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document.write( "Now, since (x - 2)(x + 1) > 0 implies that either x - 2 > 0 or x + 1 > 0 , the<BR>\n" );
document.write( "solution to the inequality must be the interval (-1,&#8734;).\r<BR>\n" );
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document.write( "c) Solution 3<BR>\n" );
document.write( "Since (x - 2)(x + 1) > 4 means that (x - 2)(x + 1) - 4 > 0 , and (x - 2)(x + 1) - 4 > 0 is equivalent to writing x^2 - x - 6 > 0 and x^2 - x - 6 = 0 when x = -2 and x = 3 ,the solution to the inequality must be the interval (-2,3).\r<BR>\n" );
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document.write( "d) Solution 4<BR>\n" );
document.write( "Since (x - 2)(x + 1) > 4 means that (x - 2)(x + 1) - 4 > 0 , and (x - 2)(x + 1) - 4 > 0 is equivalent to writing x^2 - x - 6 > 0 and x^2 - x - 6 = 0 when x = -2 and x = 3 , the solution to the inequality must be the interval (-&#8734;,-2)and(3,&#8734;) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #270679 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=270679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Which of the following solutions to the quadratic inequality <BR>\n" );
document.write( "(x - 2)(x + 1) > 4 <BR>\n" );
document.write( "is correct? Explain why the others are incorrect. <BR>\n" );
document.write( "a) Solution 1<BR>\n" );
document.write( "Since (x - 2)(x + 1) > 4 means that x - 2 > 4 or x + 1 > 4 ,we have the following: <BR>\n" );
document.write( "if x - 2 > 4 , then x > 6 and if x + 1 > 4 , then x > 3.<BR>\n" );
document.write( "Therefore the solution to the inequality is the interval (3,&#8734;).<BR>\n" );
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document.write( "But x= -3 is also a solution: and x=-4, or x= -5, etc.<BR>\n" );
document.write( "And they are not in (3,+inf)<BR>\n" );
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document.write( "b) Solution 2<BR>\n" );
document.write( "Since (x - 2)(x + 1) > 4 means that (x - 2)(x + 1) - 4 > 0 , we have the following: <BR>\n" );
document.write( "Either (x - 2)(x + 1) > 0 or -4 > 0 and since -4 is never greater than 0 we<BR>\n" );
document.write( "need only worry about (x - 2)(x + 1) > 0 .<BR>\n" );
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document.write( "No: (x-2)(x+1) >4, not just > 0.<BR>\n" );
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document.write( "Now, since (x - 2)(x + 1) > 0 implies that either x - 2 > 0 or x + 1 > 0 , the<BR>\n" );
document.write( "solution to the inequality must be the interval (-1,&#8734;).<BR>\n" );
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document.write( "c) Solution 3<BR>\n" );
document.write( "Since (x - 2)(x + 1) > 4 means that (x - 2)(x + 1) - 4 > 0 , and (x - 2)(x + 1) - 4 > 0 is equivalent to writing x^2 - x - 6 > 0 and x^2 - x - 6 = 0 when x = -2 and x = 3 ,the solution to the inequality must be the interval (-2,3).<BR>\n" );
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document.write( "No. -2 and 3 are the boundary values of the solution set of the inequality<BR>\n" );
document.write( "The solution sets are to the left of -2 and the right of 3.<BR>\n" );
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document.write( "d) Solution 4<BR>\n" );
document.write( "Since (x - 2)(x + 1) > 4 means that (x - 2)(x + 1) - 4 > 0 , and (x - 2)(x + 1) - 4 > 0 is equivalent to writing x^2 - x - 6 > 0 and x^2 - x - 6 = 0 when x = -2 and x = 3 , the solution to the inequality must be the interval (-&#8734;,-2)and(3,&#8734;)<BR>\n" );
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document.write( "True<BR>\n" );
document.write( "============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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