document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971159>Question 971159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve and graph the solution of the two inequalities <BR>\n" );
document.write( "|3x-7|is equal or greater than 23\r<BR>\n" );
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document.write( "(X-1)(x+3)(x2)<0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593790 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=593790\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> |3x-7| >= 23.\r<BR>\n" );
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document.write( "if the expression inside the absolute value sign is positive, then the absolute value of the expression is equal to the expression itself.\r<BR>\n" );
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document.write( "if the expression insides the absolute value sign is negative, then the absolute value of the expression is equal to the expression iteslf times - 1.\r<BR>\n" );
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document.write( "what this means is that you split the problem into two pieces.\r<BR>\n" );
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document.write( "you get 3x-7 >= 23 and you get -(3x-7) >= 23\r<BR>\n" );
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document.write( "when you take -(3x-7) >= 23 and multiply both sides of that equation by -1, you wind up with 3x-7 <= -23.\r<BR>\n" );
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document.write( "so you are dealing with 3x - 7 >= 23 and you are dealing with 3x-7 <= 23\r<BR>\n" );
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document.write( "solve 3x-7 >= 23 to get x >= 10.\r<BR>\n" );
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document.write( "solve 3x-7 <= -23 to get x <= -16/3\r<BR>\n" );
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document.write( "those are your solutions.\r<BR>\n" );
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document.write( "for (x-1)(x+3)(x^2) < 0, set it equal and solve for x.\r<BR>\n" );
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document.write( "you will get x = 1, x = -3, and x = 0.\r<BR>\n" );
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document.write( "those are the transition points in the grpah of that equation.\r<BR>\n" );
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document.write( "look at the intervals to the left of x = -3, between -3 and 0, between 0 and 1, and greater than 1.\r<BR>\n" );
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document.write( "see if the function is positive or negative in those intervals.\r<BR>\n" );
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document.write( "when x = -5, the function is positive.<BR>\n" );
document.write( "when x = -1, the function is negative.<BR>\n" );
document.write( "when x = .5, the function is negative.<BR>\n" );
document.write( "when x = 5, the function is positive.\r<BR>\n" );
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document.write( "your solution should be that the function is negative between x = -3 and 0 and between x = 0 and x = 1\r<BR>\n" );
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document.write( "this can be written as:\r<BR>\n" );
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document.write( "-3 < x < 0 and 0 < x < 1\r<BR>\n" );
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document.write( "you can't include -3 or 0 or 1 because the function is < 0 and not <= 0.\r<BR>\n" );
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document.write( "here's a graph of the equation of y = (x-1)*(x+4)*(x^2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-5%2C5%2C%28x-1%29%28x%2B3%29%28x%5E2%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-5%2C5%2C%28x-1%29%28x%2B3%29%28x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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