document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1071816>Question 1071816</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the answer of |3x+4|+|2x+1|+|x+1|=12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #686723 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=686723\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> well, one of the answers is 1.<BR>\n" );
document.write( "you just take away the positive value sign and solve for x and you get 1.<BR>\n" );
document.write( "the expression inside the positive value sign can be negative.<BR>\n" );
document.write( "you would get -(x + 1) - (3x+4) - (2x+1) - (x+1) = 12<BR>\n" );
document.write( "that becomes:<BR>\n" );
document.write( "- 3x - 4 - 2x - 1 - x - 1 = 12<BR>\n" );
document.write( "combine like terms to get: -6x - 6 = 12<BR>\n" );
document.write( "add 6 to both sides to get -6x = 18<BR>\n" );
document.write( "solve for x to get x = -3\r<BR>\n" );
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document.write( "so, if i did this right, x = 1 or x = -3.\r<BR>\n" );
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document.write( "you can also solve it graphically.\r<BR>\n" );
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document.write( "your graph would look like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/030701.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "abs(x) means the same thing as |x| to this graphing software.\r<BR>\n" );
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document.write( "the main idea is that if the absolute value of an expression is equal to something, then either that expression is equal to that something or that expression times -1 is equal to that something.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "abs(3x+4) = 7\r<BR>\n" );
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document.write( "either (3x+4) = 7 or -(3x+4) = 7\r<BR>\n" );
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document.write( "this gets you x = 1 or x =  -11/3\r<BR>\n" );
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document.write( "the books will usually show you that:\r<BR>\n" );
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document.write( "abs(x) = x and abs (x) = -x\r<BR>\n" );
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document.write( "what they are talking about is the expression inside the absolute value sign, an not just the value of x.\r<BR>\n" );
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document.write( "therefore:\r<BR>\n" );
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document.write( "abs(x + a) = x + a and abs(x) = -(x + a).\r<BR>\n" );
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document.write( "i used that fact to solve this problem.\r<BR>\n" );
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document.write( "the expression inside the absolute value sign will either be positive or it will be negative.\r<BR>\n" );
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document.write( "you will also see:\r<BR>\n" );
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document.write( "if abs(x+a) > y, then (x+a) > y and (x+a) < -y.\r<BR>\n" );
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document.write( "this also stems from what i just told you.\r<BR>\n" );
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document.write( "in my interpretation:\r<BR>\n" );
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document.write( "(x+a) > y and -(x+a) > y\r<BR>\n" );
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document.write( "in the second inequality, just multiply both sides of the inequality by -1 and you will get (x+a) < -y\r<BR>\n" );
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document.write( "the books have done that extra step for you but do not usually explain why it is that way.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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