document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=978999>Question 978999</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question is solve the inequality for Algebra II<BR>\n" );
document.write( " 3x-4/x+3<2 what is the solution? May I have step by step. Thank you so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #600328 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52814)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=600328\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "1. &nbsp;Let us assume that the denominator &nbsp;x+3&nbsp; is greater than &nbsp;0:\r<BR>\n" );
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document.write( "x + 3 > 0, &nbsp;&nbsp;&nbsp;&nbsp;i.e. &nbsp;&nbsp;x > -3.\r<BR>\n" );
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document.write( "Then the inequality &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-4%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%283x-4%29%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; is equivalent to the inequality \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-4 ALIGN=MIDDLE  ALT=\"3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "(we simply multiplied both sides of the original inequality by the positive multiplier - denominator, and kept the sign of the inequality &nbsp;\"as is\").\r<BR>\n" );
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document.write( "Solve it step by step:\r<BR>\n" );
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document.write( "3x - 4 < 2x + 6,\r<BR>\n" );
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document.write( "x < 6 + 4 = 10.\r<BR>\n" );
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document.write( "Thus &nbsp;-3 < x < 10&nbsp; is the solution of the given inequality.\r<BR>\n" );
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document.write( "2. &nbsp;Next, assume that the denominator &nbsp;x+3&nbsp; is lesser than &nbsp;0:\r<BR>\n" );
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document.write( "x + 3 < 0, &nbsp;&nbsp;&nbsp;&nbsp;i.e. &nbsp;&nbsp;x < -3.\r<BR>\n" );
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document.write( "Then the inequality &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-4%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%283x-4%29%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; is equivalent to the inequality \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-4 ALIGN=MIDDLE  ALT=\"3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "(we simply multiplied both sides of the original inequality by the negative multiplier - denominator, &nbsp;and accordingly changed the sign of the inequality to the opposite one).\r<BR>\n" );
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document.write( "Solve it step by step:\r<BR>\n" );
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document.write( "3x - 4 > 2x + 6,\r<BR>\n" );
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document.write( "x > 6 + 4 = 10.\r<BR>\n" );
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document.write( "Thus this alternative lead us to the two two inequalities x < -3  and x > 10. &nbsp;Obviously, they can not be true simultaneously. &nbsp;So, &nbsp;this alternative has no solution.\r<BR>\n" );
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document.write( "The only solution is the first alternative solved in n.1.\r<BR>\n" );
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document.write( "<B>Answer</B>. The solution of the given inequality is &nbsp;-3 < x < 10.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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