document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148112>Question 148112</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Product of two consecutive  positive intergers is 1 more than their sum. Find the intergers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108509 by </B><A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><B>Electrified_Levi(103)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><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=108509\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, Hope I can help,<BR>\n" );
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document.write( "The Product of two consecutive positive integers is 1 more than their sum. Find the integers.<BR>\n" );
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document.write( "The first integer is \"x\", the second is (x+1)<BR>\n" );
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document.write( "consecutive means one after the other, if there was a third, fourth, and fifth integer it would be (x+2),(x+3),(x+4)(You will do this on any problem where it says consecutive(unless it says consecutive odd, or even, then you add \"2\" each time<BR>\n" );
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document.write( "Now we can do the equation<BR>\n" );
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document.write( "The Product of two consecutive positive integers is 1 more than their sum. <BR>\n" );
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document.write( "(x)(x+1) = (x)+(x+1)+1<BR>\n" );
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document.write( "We will use the distributive property<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2Bx+=+%28x%29%2B%28x%2B1%29%2B1+ ALIGN=MIDDLE  ALT=\"+x%5E2%2Bx+=+%28x%29%2B%28x%2B1%29%2B1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2Bx+=+x%2Bx%2B1%2B1+ ALIGN=MIDDLE  ALT=\"+x%5E2%2Bx+=+x%2Bx%2B1%2B1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2Bx+=+2x%2B2+ ALIGN=MIDDLE  ALT=\"+x%5E2%2Bx+=+2x%2B2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will move everything on the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2Bx+-+2x+-2+=+2x+-2x%2B2-2+ ALIGN=MIDDLE  ALT=\"+x%5E2%2Bx+-+2x+-2+=+2x+-2x%2B2-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+x+-+2+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+x+-+2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+x+-+2+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+x+-+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > has factors of (x+1), and (x-2) ( factors of (-2) add up to (-1))<BR>\n" );
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document.write( "We can now solve for \"x\", using one factor at a time.<BR>\n" );
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document.write( "First factor<BR>\n" );
document.write( "(x+1)=0<BR>\n" );
document.write( "x+1=0<BR>\n" );
document.write( "x+1-1=0-1<BR>\n" );
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document.write( "x=(-1)<BR>\n" );
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document.write( "Second factor<BR>\n" );
document.write( "(x-2)=0<BR>\n" );
document.write( "x-2=0<BR>\n" );
document.write( "x-2+2=0+2<BR>\n" );
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document.write( "x = 2<BR>\n" );
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document.write( "You can check by replacing \"x\" with (-1), or 2, in the equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+x+-+2+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+x+-+2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( We will only check one answer, (2)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5E2+-+2+-+2+=+0+ ALIGN=MIDDLE  ALT=\"+2%5E2+-+2+-+2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+-+2+-+2+=+0+ ALIGN=MIDDLE  ALT=\"+4+-+2+-+2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+0+ ALIGN=MIDDLE  ALT=\"+0+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "The first integer is x, or 2(It asked for a positive integer), the second integer is (x+1), or 3<BR>\n" );
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document.write( "You can check by replacing \"x\" with 2 in <BR>\n" );
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document.write( "(x)(x+1) = (x)+(x+1)+1<BR>\n" );
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document.write( "(2)(2+1) = (2)+(2+1)+1<BR>\n" );
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document.write( "(2)(3) = (2)+(3)+1<BR>\n" );
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document.write( "6 = 6<BR>\n" );
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document.write( "First integer = 2<BR>\n" );
document.write( "Second integer = 3<BR>\n" );
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document.write( "Hope I helped, Levi </SPAN>\n" );
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