document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126650>Question 126650</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find 2 consecutive even integers whose product is 48. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92823 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=92823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consecutive even numbers can be represented by x for the first and the next number has to be<BR>\n" );
document.write( "2 more than that. So the next even number is x + 2. (Think of 6 and 8 as being consecutive<BR>\n" );
document.write( "even numbers ... and note that they are 2 units apart.)<BR>\n" );
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document.write( "You are now told that the product of these two consecutive even numbers is 48. So multiply the<BR>\n" );
document.write( "two numbers together and set the result equal to 48 as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B2%29+=+48 ALIGN=MIDDLE  ALT=\"x%28x%2B2%29+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply out the left side and this equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2x+=+48 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2x+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get this into standard quadratic form by subtracting 48 from both sides and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2x+-+48+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2x+-+48+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The left side of this equation can be factored as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+8%29%28x+-+6%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+8%29%28x+-+6%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice this equation will be true if either of the two factors on the left side equals zero<BR>\n" );
document.write( "because a multiplication by zero will make the entire left side become zero and therefore<BR>\n" );
document.write( "equal to the right side.<BR>\n" );
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document.write( "Set the two factors equal to zero (one at a time) as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+8+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for x by subtracting 8 from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-8 ALIGN=MIDDLE  ALT=\"x+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "then set the other factor equal to zero to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+6+=+0 ALIGN=MIDDLE  ALT=\"x+-+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve by adding 6 to both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6 ALIGN=MIDDLE  ALT=\"x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So there are two possible answers to this problem because x (the first of the consecutive<BR>\n" );
document.write( "even integers) can either be -8 or + 6. \r<BR>\n" );
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document.write( "This means that in the first possible set of consecutive even integers you have -8 and as the <BR>\n" );
document.write( "first integer and therefore the next consecutive integer is 2 greater than that or -6. These <BR>\n" );
document.write( "numbers are consecutive and even and their product is +48.<BR>\n" );
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document.write( "For the second answer you have that the first integer (x) is +6 and therefore the next <BR>\n" );
document.write( "consecutive integer is +8. This pair (+6 and +8) are consecutive and even and their product <BR>\n" );
document.write( "is also +48.<BR>\n" );
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document.write( "So the two answers are either -8 and -6 or +6 and +8.<BR>\n" );
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document.write( "Hope this helps you to see how this problem can be worked.<BR>\n" );
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