document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=7770>Question 7770</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can amyone help me figure out this Absolute Value problem:\r<BR>\n" );
document.write( "\n" );
document.write( " 4-3 | x - 2 | = -8\r<BR>\n" );
document.write( "\n" );
document.write( "I'm sure it is simple but it is not so simple for me tonight.\r<BR>\n" );
document.write( "\n" );
document.write( "Please expalin steps to isolate the absolute value. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4273 by </B><A HREF=/tutors/aboutme.mpl?userid=prince_abubu><B>prince_abubu(198)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=prince_abubu><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=4273\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Alright. The 4 is not being multiplied by the absolute value, so move it to the right by subtracting it. So far, you should get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3abs%28x-2%29+=+-12+ ALIGN=MIDDLE  ALT=\"+-3abs%28x-2%29+=+-12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- combined the -4 and the -8.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+abs%28x-2%29+=+4+ ALIGN=MIDDLE  ALT=\"+abs%28x-2%29+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- divide both sides by -3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now here's the tricky part. Just by looking at it, it's so tempting to say that x = 6 because 6 - 4 = 2. And that's right. BUT, there is ANOTHER solution!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Actually, when you solve absolute value equations, you actually solve 2 equations. In this case, the two are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+2+=+4+ ALIGN=MIDDLE  ALT=\"+x+-+2+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which was what we did, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+2+=+-4+ ALIGN=MIDDLE  ALT=\"+x+-+2+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Why, though, do we do that!?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We know that |4| = 4, right? So we set the inside of the absolute value x - 2 to equal four. BUT we also know that |-4| = 4. AHA! So it then makes sense to set the inside of the absolute value equal to -4. After all, it'll turn that -4 into a positive 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "SO, let's nail down the x - 2 = -4 also. It turns out (by adding 2 to both sides) that x = -2. If we plugged that into the absolute value, we have |-2 - 2| = |-4| = 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So your solutions are 6 and -2. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );