document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202532>Question 1202532</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve each equations & inequality with absolute value<BR>\n" );
document.write( "a)|2x+1|-3=12<BR>\n" );
document.write( "b)|3x+1|+2<6<BR>\n" );
document.write( "c)|1/3x+7|+5>6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837426 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=837426\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll do part (a) to get you started.\r<BR>\n" );
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document.write( "We'll need the rule that |x| = k leads to x = k or x = -k, where k > 0.<BR>\n" );
document.write( "Example: |x| = 7 leads to x = 7 or x = -7. <BR>\n" );
document.write( "Both values are the same distance to zero on the number line.\r<BR>\n" );
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document.write( "|2x+1|-3 = 12<BR>\n" );
document.write( "|2x+1| = 12+3<BR>\n" );
document.write( "|2x+1| = 15<BR>\n" );
document.write( "2x+1 = 15 or 2x+1 = -15 ... use the rule mentioned above<BR>\n" );
document.write( "2x = 15-1 or 2x = -15-1<BR>\n" );
document.write( "2x = 14 or 2x = -16<BR>\n" );
document.write( "x = 14/2 or x = -16/2<BR>\n" );
document.write( "<font color=red>x = 7 or x = -8</font> \r<BR>\n" );
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document.write( "-----------------------------\r<BR>\n" );
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document.write( "Slightly another way to solve<BR>\n" );
document.write( "Let w = |2x+1|\r<BR>\n" );
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document.write( "The equation <BR>\n" );
document.write( "|2x+1|-3 = 12<BR>\n" );
document.write( "becomes<BR>\n" );
document.write( "w-3 = 12<BR>\n" );
document.write( "which solves to<BR>\n" );
document.write( "w = 15\r<BR>\n" );
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document.write( "That's another way to arrive at the step |2x+1| = 15<BR>\n" );
document.write( "The remaining steps are the same as the previous section.\r<BR>\n" );
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document.write( "Answer to part (a): <font color=red>x = 7 or x = -8</font>\r<BR>\n" );
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document.write( "Hint for part (b): If |x| < k then -k < x < k, where k is positive. <BR>\n" );
document.write( "Example: |x| < 5 means -5 < x < 5.\r<BR>\n" );
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document.write( "Hint for part (c): If |x| > k then x < -k or x > k, where k is positive. <BR>\n" );
document.write( "Example: |x| > 12 means either x < -12 or x > 12.\r<BR>\n" );
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document.write( "Another hint: Draw out number lines to see why those formulas work the way they do.<BR>\n" );
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