document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151023>Question 1151023</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If (x+1)(x-2) is positive, which statement must be true?<BR>\n" );
document.write( "A. x<-1 or x>2<BR>\n" );
document.write( "B. x>-1 or x<2<BR>\n" );
document.write( "C. -1<x<2<BR>\n" );
document.write( "D. -2<x<1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #772616 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=772616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "A shorthand way of saying \"(x+1)(x-2) is positive\" is to write (x+1)(x-2) > 0\r<BR>\n" );
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document.write( "Change the inequality sign to an equal sign. Then solve for x using the zero product property.\r<BR>\n" );
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document.write( "(x+1)(x-2) = 0<BR>\n" );
document.write( "x+1 = 0 or x-2 = 0<BR>\n" );
document.write( "x = -1 or x = 2\r<BR>\n" );
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document.write( "If x = -1 or x = 2, then (x+1)(x-2) is equal to zero.\r<BR>\n" );
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document.write( "Draw a number line. Plot -1 and 2 on the number line. This drawing is optional, but it might help you see the three distinct regions.<BR>\n" );
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document.write( "Region A in red represents everything to the left of -1. <BR>\n" );
document.write( "Let's pick one value from this region, say x = -2<BR>\n" );
document.write( "(x+1)(x-2) > 0<BR>\n" );
document.write( "(-2+1)(-2-2) > 0 ... plug in x = -2<BR>\n" );
document.write( "(-1)(-4) > 0<BR>\n" );
document.write( "4 > 0<BR>\n" );
document.write( "The last inequality is true, so any value less than -1 will make (x+1)(x-2) > 0 true.\r<BR>\n" );
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document.write( "Move onto region B in blue. This is the set of numbers between -1 and 2. Pick something from this region, say  x = 0, and plug it in to get<BR>\n" );
document.write( "(x+1)(x-2) > 0<BR>\n" );
document.write( "(0+1)(0-2) > 0<BR>\n" );
document.write( "(1)(-2) > 0<BR>\n" );
document.write( "-2 > 0<BR>\n" );
document.write( "The last inequality is false, so any value between -1 and 2 will make (x+1)(x-2) > 0 false.\r<BR>\n" );
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document.write( "Finally let's check region C in green. Pick a value to the right of 2. I'll pick x = 3.<BR>\n" );
document.write( "(x+1)(x-2) > 0<BR>\n" );
document.write( "(3+1)(3-2) > 0<BR>\n" );
document.write( "(4)(1) > 0<BR>\n" );
document.write( "4 > 0<BR>\n" );
document.write( "The last inequality is true, so any value larger than 2 will make (x+1)(x-2) > 0 true.\r<BR>\n" );
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document.write( "---------------------------------------------\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "<ul><li>if x < -1, then (x+1)(x-2) > 0 is true.</li><li>if -1 < x < 2, then (x+1)(x-2) > 0 is false.</li><li>if x > 2, then (x+1)(x-2) > 0 is true.</li></ul>\r<BR>\n" );
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document.write( "This is why the final answer is A. x < -1 or x > 2<BR>\n" );
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