document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=284835>Question 284835</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I solve problems like this; 1/6(3x+10>5/12(x-1)? I'm having a hard time understanding these types of problems\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #206630 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=206630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You solve these the same way you would solve equality equations.\r<BR>\n" );
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document.write( "The only difference is that when you multiply both sides of the equation by a negative number, the inequality reverses.\r<BR>\n" );
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document.write( "Example:\r<BR>\n" );
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document.write( "6 > 5\r<BR>\n" );
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document.write( "Multiply both sides of this equation by -1 to get:\r<BR>\n" );
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document.write( "-6 < -5\r<BR>\n" );
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document.write( "The equality reversed.\r<BR>\n" );
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document.write( "If you had multiplied:\r<BR>\n" );
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document.write( "6 > 5 by -10, the equality would still have reversed.\r<BR>\n" );
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document.write( "You would have gotten:\r<BR>\n" );
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document.write( "-60 < -50\r<BR>\n" );
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document.write( "Other than that, you treat them the same way you would treat an equality equation.\r<BR>\n" );
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document.write( "Your problem is:\r<BR>\n" );
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document.write( "(1/6)*(3x+10 > (5/12)*(x-1)\r<BR>\n" );
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document.write( "Multiply both sides of this equation by 12.\r<BR>\n" );
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document.write( "This will remove the fractions on each side of the equation.\r<BR>\n" );
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document.write( "You will get:\r<BR>\n" );
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document.write( "2*(3x+10) > 5*(x-1)\r<BR>\n" );
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document.write( "Simplify by removing the parentheses to get:\r<BR>\n" );
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document.write( "6x + 20 > 5x - 5\r<BR>\n" );
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document.write( "Now you want to get all the x terms on the left side of the equation and all the constants on the right side of the equation.\r<BR>\n" );
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document.write( "Subtract 20 from both sides of the equation and subtract 5x from both sides of the equation to get:\r<BR>\n" );
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document.write( "6x - 5x > -5 - 20\r<BR>\n" );
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document.write( "Simplify to get\r<BR>\n" );
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document.write( "x > -25\r<BR>\n" );
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document.write( "That's your answer.\r<BR>\n" );
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document.write( "Notice that, since  you did not have to multiply (or divide) both sides of the equation by a negative number, the inequality did not reverse.\r<BR>\n" );
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document.write( "To confirm this answer is good, substitute it in your original equation to see if that equation is true.\r<BR>\n" );
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document.write( "Your original equation is:\r<BR>\n" );
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document.write( "(1/6)*(3x+10 > (5/12)*(x-1)\r<BR>\n" );
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document.write( "If x = -25, this equation becomes:\r<BR>\n" );
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document.write( "(1/6)*(-65) > (5/12)*(-26)\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "-65/6 > -130/12 which is equivalent to:\r<BR>\n" );
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document.write( "-65/6 > -65/6\r<BR>\n" );
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document.write( "They are equal to the equation is false when x = -25.\r<BR>\n" );
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document.write( "The equation should be false when x = -25, because the answer is that x > -25.\r<BR>\n" );
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document.write( "Pick any value of x > -25 and the equation should be true.\r<BR>\n" );
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document.write( "We'll try something simple, like -20\r<BR>\n" );
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document.write( "The original equation is:\r<BR>\n" );
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document.write( "(1/6)*(3x+10 > (5/12)*(x-1)\r<BR>\n" );
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document.write( "When x = -20, this becomes:\r<BR>\n" );
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document.write( "(1/6)*(-50) > (5/12)*(-21)\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "-50/6 > -105/12\r<BR>\n" );
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document.write( "This is equivalent to:\r<BR>\n" );
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document.write( "-100/12 > -105/12\r<BR>\n" );
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document.write( "-100/12 is greater than -105/12 (It is more positive), so the equation is true which confirms that as long as x > -25, the original equation will be true, and as long as x is not > -25, the original equation is false.\r<BR>\n" );
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document.write( "Your answer is that x > -25.\r<BR>\n" );
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