document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=230867>Question 230867</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the answer to |3-4x|-3<=8 ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #170984 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=170984\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Equation is |3-4x| - 3 <= 8\r<BR>\n" );
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document.write( "This means that if the expression within the absolute value sign is positive, then:\r<BR>\n" );
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document.write( "3-4x - 3 <= 8\r<BR>\n" );
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document.write( "Combine like terms to get:\r<BR>\n" );
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document.write( "-4x <= 8\r<BR>\n" );
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document.write( "Divide both sides by 4 to get:\r<BR>\n" );
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document.write( "-x <= 2\r<BR>\n" );
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document.write( "Multiply both sides by -1 to get:\r<BR>\n" );
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document.write( "x >= -2\r<BR>\n" );
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document.write( "Note that the inequality is reversed when you multiply both sides by -1.\r<BR>\n" );
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document.write( "If the expression within the absolute value sign is negative, then:\r<BR>\n" );
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document.write( "-(3-4x) - 3 <= 8\r<BR>\n" );
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document.write( "This becomes:\r<BR>\n" );
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document.write( "-3 + 4x - 3 <= 8\r<BR>\n" );
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document.write( "Combine like terms to get:\r<BR>\n" );
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document.write( "-6 + 4x <= 8\r<BR>\n" );
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document.write( "Add 6 to both sides of the equation to get:\r<BR>\n" );
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document.write( "4x <= 8+6 becomes 4x <= 14\r<BR>\n" );
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document.write( "Divide both sides of the equation by 4 to get:\r<BR>\n" );
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document.write( "x <= 14/4\r<BR>\n" );
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document.write( "You have:\r<BR>\n" );
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document.write( "x >= -2\r<BR>\n" );
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document.write( "and:\r<BR>\n" );
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document.write( "x <= 14/4\r<BR>\n" );
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document.write( "This is equivalent to -2 <= x <= 14/4\r<BR>\n" );
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document.write( "We need to confirm these values are accurate.\r<BR>\n" );
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document.write( "We'll take values inside and outside the limits to see what happens.\r<BR>\n" );
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document.write( "We'll do:\r<BR>\n" );
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document.write( "x = -3 (outside limits)<BR>\n" );
document.write( "x = -2 (within limits)<BR>\n" );
document.write( "x = 3 (within limits)<BR>\n" );
document.write( "x = 14/4 (within limits)<BR>\n" );
document.write( "x = 4 (outside limits)\r<BR>\n" );
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document.write( "When x = -3, |3-4x| - 3 = |3+12| - 3 = |15| - 3 = 15-3 = 12 > 8 so this is NOT ok as it should be.\r<BR>\n" );
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document.write( "When x = -2, |3-4x| - 3 = |3+8| - 3 = |11| - 3 = 11 - 3 = 8 <= 8 so this IS ok as it should be.\r<BR>\n" );
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document.write( "When x = 3, |3-4x| - 3 = |3-12| - 3 = |-9| - 3 = 9 - 3 = 6 <= 8 so this IS ok as it should be.\r<BR>\n" );
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document.write( "When x = 14/4, |3-4x| - 3 = |3 - 14| - 3 = |-11| - 3 = 11 - 3 = 8 <= 8 so this IS ok as it should be.\r<BR>\n" );
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document.write( "When x = 4, |3-4x| - 3 = |3 - 16| - 3 = |-13| - 3 = 13 - 3 = 10 > 8 so this is NOT ok as it should be.\r<BR>\n" );
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document.write( "Looks likes these values are good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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