document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=10819>Question 10819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation:  <BR>\n" );
document.write( "19 -(2x +3) = 2(x + 3) +x\r<BR>\n" );
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document.write( "My attempt:<BR>\n" );
document.write( "19 - (2x + 3) = 2(x + 3) +x<BR>\n" );
document.write( "19 - 2x + 3 = 2x + 3 +x<BR>\n" );
document.write( "19 - 2x + 3 = 3x + 3<BR>\n" );
document.write( "19 - 2x + 3 - 3x = + 3<BR>\n" );
document.write( "19 +3 -3 = +3 -3<BR>\n" );
document.write( "19 = x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5690 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=5690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sorry, but your attempt is riddled with wrong algebra.\r<BR>\n" );
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document.write( "First thing is to understand what the question actually says, because from your working, you do not understand. I think you wildly do stuff and hope for the best.\r<BR>\n" );
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document.write( "19 - (2x +3) = 2(x + 3) +x is a shortened version (yes, a lazy version even) for<BR>\n" );
document.write( "19 -1*(2x +3) = 2*(x + 3) + 1*x\r<BR>\n" );
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document.write( "Mathematicians tend not to write a \"1\" or a \"*\" when we do not need too. But you have to remember they are there.\r<BR>\n" );
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document.write( "Secondly, you have to know what to do when you have brackets... the second bracker for example says \"we have (x+3) and we multiply these terms by 2. So we will get a \"2x\" and a \"6\" when we expand the bracket.\r<BR>\n" );
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document.write( "Similarly, with the first bracket, we have the (2x+3) and we have to multiply both terms by the -1... giving us -2x and -3. ALWAYS BE CAREFUL with brackets and negatives outside!\r<BR>\n" );
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document.write( "So, we get:<BR>\n" );
document.write( "19 - (2x +3) = 2(x + 3) + x<BR>\n" );
document.write( "19 - 2x - 3 = 2x + 6 + x\r<BR>\n" );
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document.write( "Now collect like terms together:<BR>\n" );
document.write( "19 - 2x - 3 = 2x + 6 + x<BR>\n" );
document.write( "16 - 2x = 3x + 6\r<BR>\n" );
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document.write( "Now move terms so that all variables (here, the x-terms) are on one side and the numbers are on the other side:<BR>\n" );
document.write( "16 - 2x = 3x + 6 --> Add 2x to both sides.<BR>\n" );
document.write( "16 = 5x + 6\r<BR>\n" );
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document.write( "or, 5x + 6 = 16 \r<BR>\n" );
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document.write( "--> now we subtract 6 from both sides to give<BR>\n" );
document.write( "5x = 10\r<BR>\n" );
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document.write( "--> now, we have 5x, like 5 apples. So, if 5 apples cost 10pence, one apple must cost 2p, yes? How did I do that? I divided both sides by 5.\r<BR>\n" );
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document.write( "Why did i divide both sides by 5? because i had 5*x and i want to know 1*x. So i have to mess with the 5 without messing the x, so 5/5 is 1. And the one rule of algebra that i have used abouve too, is that \"whatever you do to one side, you HAVE to do to the other side\", so we have 10 and must divide that by 5 too.\r<BR>\n" );
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document.write( "so, 5x = 10<BR>\n" );
document.write( "then x = 10/5<BR>\n" );
document.write( "--> x= 2\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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