document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=209593>Question 209593</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each equation. Check for extraneous solutions.\r<BR>\n" );
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document.write( "Equation: |5x-1|+7=3x\r<BR>\n" );
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document.write( "Here's what I did:\r<BR>\n" );
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document.write( "|5x-1|+7=3x<BR>\n" );
document.write( "      -7 -7\r<BR>\n" );
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document.write( "|5x+1|=3x-7\r<BR>\n" );
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document.write( "5x-1=3x-7 OR 5x-1=-(3x-7)<BR>\n" );
document.write( "  +1   +1    <BR>\n" );
document.write( "               <BR>\n" );
document.write( "5x=3x-6         <BR>\n" );
document.write( "-3x -3x      <BR>\n" );
document.write( "             <BR>\n" );
document.write( "2x=-6       <BR>\n" );
document.write( "--  --       <BR>\n" );
document.write( "2   2        <BR>\n" );
document.write( "              <BR>\n" );
document.write( "x=-3\r<BR>\n" );
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document.write( "OR<BR>\n" );
document.write( "5x-1=-(3x-7)<BR>\n" );
document.write( "5x-1=-3x\r<BR>\n" );
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document.write( "So, x=-3 or x=1.\r<BR>\n" );
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document.write( "CHECK:<BR>\n" );
document.write( "|5x-1|+7=3x<BR>\n" );
document.write( "|5(-3)-1|+7=+3(-3)<BR>\n" );
document.write( "|-15-1|+7=-9<BR>\n" );
document.write( "|-16|+7=-9 <BR>\n" );
document.write( "16+7=-9<BR>\n" );
document.write( "23=9<BR>\n" );
document.write( "But 23 doesn't equal 9. At first I thought it was just an exraneous solution. But then I checked the second number:\r<BR>\n" );
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document.write( "|5x-1|+7=3x<BR>\n" );
document.write( "|5(1)-1|+7=3(1)<BR>\n" );
document.write( "|5-1|+7=3<BR>\n" );
document.write( "|4|+7=3<BR>\n" );
document.write( "4+7=3<BR>\n" );
document.write( "11=3<BR>\n" );
document.write( "But again, 11 doesn't equal 3. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #158488 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=158488\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve each equation. Check for extraneous solutions. <BR>\n" );
document.write( "Equation: |5x-1|+7=3x <BR>\n" );
document.write( "Here's what I did: <BR>\n" );
document.write( "|5x-1|+7=3x<BR>\n" );
document.write( "-7 -7 <BR>\n" );
document.write( "|5x+1|=3x-7 <BR>\n" );
document.write( "5x-1=3x-7 OR 5x-1=-(3x-7)<BR>\n" );
document.write( "+1 +1 \r<BR>\n" );
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document.write( "5x=3x-6 <BR>\n" );
document.write( "-3x -3x \r<BR>\n" );
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document.write( "2x=-6 <BR>\n" );
document.write( "-- -- <BR>\n" );
document.write( "2 2 \r<BR>\n" );
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document.write( "x=-3 <BR>\n" );
document.write( "OR<BR>\n" );
document.write( "5x-1=-(3x-7)<BR>\n" );
document.write( "5x-1=-3x+7<BR>\n" );
document.write( "8x = 8<BR>\n" );
document.write( "x = 1 <BR>\n" );
document.write( "So, x=-3 or x=1. <BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "|5x-1|+7=3x<BR>\n" );
document.write( "|5(-3)-1|+7=+3(-3)<BR>\n" );
document.write( "|-15-1|+7=-9<BR>\n" );
document.write( "|-16|+7=-9 <BR>\n" );
document.write( "16+7=-9<BR>\n" );
document.write( "23=9<BR>\n" );
document.write( "But 23 doesn't equal 9. At first I thought it was just an exraneous solution. But then I checked the second number: <BR>\n" );
document.write( "|5x-1|+7=3x<BR>\n" );
document.write( "|5(1)-1|+7=3(1)<BR>\n" );
document.write( "|5-1|+7=3<BR>\n" );
document.write( "|4|+7=3<BR>\n" );
document.write( "4+7=3<BR>\n" );
document.write( "11=3<BR>\n" );
document.write( "But again, 11 doesn't equal 3.<BR>\n" );
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document.write( "Your work is correct.<BR>\n" );
document.write( "Both \"solution\" are extraneous.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "If you graph the left side and the right side of the equation<BR>\n" );
document.write( "separately, you will see that they do not intersect, i.e. they<BR>\n" );
document.write( "are never equal.<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "Reply to stanbon@comcast.net </SPAN>\n" );
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