document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1762>Question 1762</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help me solve this inequalities please...thanks<BR>\n" );
document.write( "Question 1:\r<BR>\n" );
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document.write( "2/3 < (x+5)/-4 < 3/2\r<BR>\n" );
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document.write( "2/3's is less than (x+5)/-4 is less than/equal to 3/2's. \r<BR>\n" );
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document.write( "Question 2:\r<BR>\n" );
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document.write( "6x+5 4x-3<BR>\n" );
document.write( "---->----<BR>\n" );
document.write( " -2 = 5\r<BR>\n" );
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document.write( "(6x+5)/2 is greater than/= to (4x-3)/5\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the thing with inequalities...they are JUST the same as equalities except for 1 important difference....if you multiply or divide by any negative number, then the inequality symbol changes round.\r<BR>\n" );
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document.write( "OK, assuming i have your questions correctly written, here are the solutions:\r<BR>\n" );
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document.write( "1. do the 2 inequalities separately, so...\r<BR>\n" );
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document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29+%3C+%28%28x%2B5%29%2F%28-4%29%29 ALIGN=MIDDLE  ALT=\"%282%2F3%29+%3C+%28%28x%2B5%29%2F%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > first cross multiply, and note that one of the multiplications is a negative number, hence the inequality swaps round.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%282%29+%3E+%283%29%28x%2B5%29 ALIGN=MIDDLE  ALT=\"%28-4%29%282%29+%3E+%283%29%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8+%3E+3x+%2B+15 ALIGN=MIDDLE  ALT=\"-8+%3E+3x+%2B+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-23+%3E+3x ALIGN=MIDDLE  ALT=\"-23+%3E+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%3C+-23 ALIGN=MIDDLE  ALT=\"3x+%3C+-23\"   DISABLED_style= \"max-width:90%; height:auto;\" >...this is EXACTLY the same line...no maths done here, i have just re-written the line with the x first, as that is \"standard\" notation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+%28-23%29%2F%283%29 ALIGN=MIDDLE  ALT=\"x+%3C+%28-23%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B5%29%2F%28-4%29%29+%3C=+%283%2F2%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B5%29%2F%28-4%29%29+%3C=+%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%28x%2B5%29+%3E=+%28-4%29%283%29 ALIGN=MIDDLE  ALT=\"%282%29%28x%2B5%29+%3E=+%28-4%29%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > again, we have multiplied by a negative, so the inequality swaps over.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B10+%3E=+-12 ALIGN=MIDDLE  ALT=\"2x%2B10+%3E=+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%3E=+-22 ALIGN=MIDDLE  ALT=\"2x+%3E=+-22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+-11 ALIGN=MIDDLE  ALT=\"x+%3E=+-11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the answer is x has to be less than -23/3 which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%282%2F3%29 ALIGN=MIDDLE  ALT=\"-7%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. x also has to be bigger or equal to -11....so the answer in maths notation is...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11+%3C=+x+%3C+%28-23%29%2F%283%29 ALIGN=MIDDLE  ALT=\"-11+%3C=+x+%3C+%28-23%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=======================================================<BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%2B5%29%2F%28-2%29+%3E+%284x-3%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%286x%2B5%29%2F%28-2%29+%3E+%284x-3%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Again we have a negative number to multiply with, so the symbol will change round...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%286x%2B5%29+%3C+%28-2%29%284x-3%29 ALIGN=MIDDLE  ALT=\"%285%29%286x%2B5%29+%3C+%28-2%29%284x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2830x%2B25%29+%3C+%28-8x%2B6%29 ALIGN=MIDDLE  ALT=\"%2830x%2B25%29+%3C+%28-8x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38x+%3C+-19 ALIGN=MIDDLE  ALT=\"38x+%3C+-19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+-%281%2F2%29 ALIGN=MIDDLE  ALT=\"x+%3C+-%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I hope this explains inequalities to you...they are very simple and you shouldn't be scared of them if you understand the basics of moving numbers around and multiplying out brackets etc.\r<BR>\n" );
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document.write( "cheers<BR>\n" );
document.write( "Jon. </SPAN>\n" );
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