document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203395>Question 1203395</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ax+ b = c solve for x <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838921 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=838921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "ax means \"a times x\"<BR>\n" );
document.write( "Adjacent letters together like this usually indicates multiplication.\r<BR>\n" );
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document.write( "We start with some unknown number x.<BR>\n" );
document.write( "We then multiply it with 'a' to get ax<BR>\n" );
document.write( "Then add on b to get ax+b\r<BR>\n" );
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document.write( "The order of this is important because we follow those operations in reverse to undo them. This will isolate x.\r<BR>\n" );
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document.write( "How do we undo the \"add b\" part? By subtracting b from both sides.<BR>\n" );
document.write( "Undoing the \"multiply by a\" part means we divide both sides by 'a'.<BR>\n" );
document.write( "These are called inverse operations.\r<BR>\n" );
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document.write( "Here are the steps to isolate x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax+%2B+b+=+c ALIGN=MIDDLE  ALT=\"ax+%2B+b+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax+%2B+b-b+=+c-b ALIGN=MIDDLE  ALT=\"ax+%2B+b-b+=+c-b\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtracted b from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax+=+c-b ALIGN=MIDDLE  ALT=\"ax+=+c-b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%2Fa+=+%28c-b%29%2Fa ALIGN=MIDDLE  ALT=\"ax%2Fa+=+%28c-b%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 'a' (we must require that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3C%3E+0 ALIGN=MIDDLE  ALT=\"a+%3C%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to avoid division by zero errors)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28c-b%29%2Fa ALIGN=MIDDLE  ALT=\"x+=+%28c-b%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > And we're done. The x is all by itself now.\r<BR>\n" );
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document.write( "Here's a slightly more concrete example\r<BR>\n" );
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document.write( "Say we had 2x+5 = 37 as our equation.<BR>\n" );
document.write( "I replaced 'a' with 2, replaced b with 5, and c with 37. <BR>\n" );
document.write( "Pick any three numbers you want. As long as 'a' is nonzero. \r<BR>\n" );
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document.write( "We'll subtract 5 from both sides to undo the \"plus 5\".<BR>\n" );
document.write( "Then divide both sides by 2 to undo the \"multiply by 2\".<BR>\n" );
document.write( "Follow PEMDAS in reverse to isolate the variable. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+5+=+37 ALIGN=MIDDLE  ALT=\"2x+%2B+5+=+37\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+5-5+=+37-5 ALIGN=MIDDLE  ALT=\"2x+%2B+5-5+=+37-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 5 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+37-5 ALIGN=MIDDLE  ALT=\"2x+=+37-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F2+=+%2837-5%29%2F2 ALIGN=MIDDLE  ALT=\"2x%2F2+=+%2837-5%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divided both sides by 2\r<BR>\n" );
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document.write( "I'll leave the right hand side unevaluated so you can see how it fits the format <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c-b%29%2Fa ALIGN=MIDDLE  ALT=\"%28c-b%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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