document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198874>Question 198874</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do i answer these questions? I am trying to help my daughter and can't remember.<BR>\n" );
document.write( "2(x+4)+3x=12 \r<BR>\n" );
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document.write( "On the next one, I can't remember if add the opposite would be add positive 5 to negative 17, yielding 12 or if it would be add -5 yielding -22<BR>\n" );
document.write( "3/4x-5=-17 \r<BR>\n" );
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document.write( "How do I answer?<BR>\n" );
document.write( "2(m-3)=5(2m-6) \r<BR>\n" );
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document.write( "When do you need to reverse the inequality sign when you solve an inequality? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149361 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=149361\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B4%29%2B3x=12 ALIGN=MIDDLE  ALT=\"2%28x%2B4%29%2B3x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B8%2B3x=12 ALIGN=MIDDLE  ALT=\"2x%2B8%2B3x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B8=12 ALIGN=MIDDLE  ALT=\"5x%2B8=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=12-8 ALIGN=MIDDLE  ALT=\"5x=12-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=4 ALIGN=MIDDLE  ALT=\"5x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%29%2F%285%29 ALIGN=MIDDLE  ALT=\"x=%284%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2F5 ALIGN=MIDDLE  ALT=\"x=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > which in decimal form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.8 ALIGN=MIDDLE  ALT=\"x=0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29x-5=-17 ALIGN=MIDDLE  ALT=\"%283%2F4%29x-5=-17\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28%283%2Fcross%284%29%29x%29-4%285%29=4%28-17%29 ALIGN=MIDDLE  ALT=\"4%28%283%2Fcross%284%29%29x%29-4%285%29=4%28-17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear any fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-20=-68 ALIGN=MIDDLE  ALT=\"3x-20=-68\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=-68%2B20 ALIGN=MIDDLE  ALT=\"3x=-68%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=-48 ALIGN=MIDDLE  ALT=\"3x=-48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-48%29%2F%283%29 ALIGN=MIDDLE  ALT=\"x=%28-48%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-16 ALIGN=MIDDLE  ALT=\"x=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-16 ALIGN=MIDDLE  ALT=\"x=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "# 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28m-3%29=5%282m-6%29 ALIGN=MIDDLE  ALT=\"2%28m-3%29=5%282m-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m-6=10m-30 ALIGN=MIDDLE  ALT=\"2m-6=10m-30\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m=10m-30%2B6 ALIGN=MIDDLE  ALT=\"2m=10m-30%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m-10m=-30%2B6 ALIGN=MIDDLE  ALT=\"2m-10m=-30%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10m ALIGN=MIDDLE  ALT=\"10m\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8m=-30%2B6 ALIGN=MIDDLE  ALT=\"-8m=-30%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8m=-24 ALIGN=MIDDLE  ALT=\"-8m=-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28-24%29%2F%28-8%29 ALIGN=MIDDLE  ALT=\"m=%28-24%29%2F%28-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=3 ALIGN=MIDDLE  ALT=\"m=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=3 ALIGN=MIDDLE  ALT=\"m=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "When do you need to reverse the inequality sign when you solve an inequality?\r<BR>\n" );
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document.write( "Let's show why by example:\r<BR>\n" );
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document.write( "Let's say we have the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%3C+10 ALIGN=MIDDLE  ALT=\"1+%3C+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is true; 1 is less than 10). Now divide both sides by a negative number (say -1) to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%3C+-10 ALIGN=MIDDLE  ALT=\"-1+%3C+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which is now false (-1 is NOT less than -10). So to correct this, we simply flip the inequality sign to get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3E-10 ALIGN=MIDDLE  ALT=\"-1%3E-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and now the inequality is true again. </SPAN>\n" );
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