document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=12164>Question 12164</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Hi,<BR>\n" );
document.write( "I am learning about multiple-step equation in school and i am in Algebra-1. I was doing very well but up to this point i am confused and still don't know what i am doing wrong with my equations. We just started today and we are learning about the terms \"all reals\"(symbolized by an R w/ a line through it) and \"no solution\" (symbolized w/ an O with a slash{/} through it)Can you please help me understand what i am doing wrong with my equations. I really want to learn how so i won't be behind in my math class (lol sounds kinda nerdy but i really hoping and wanting to make a good grade in math this semester!:)) \r<BR>\n" );
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document.write( "Here is an example of one of my questions:\r<BR>\n" );
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document.write( "2(4x+1)-x=7x+2\r<BR>\n" );
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document.write( "we are suposed to find out if the answer to X<BR>\n" );
document.write( "*)has a solution...whole numbers only not fractions:)<BR>\n" );
document.write( "*)is \"all reals\"...meaning x could be any possible number <BR>\n" );
document.write( "OR<BR>\n" );
document.write( "*)has \"no solution\"... which means it has no possible answer(that a whole #)\r<BR>\n" );
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document.write( "thanks for all of your help i'd really appricate it <BR>\n" );
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 #6170 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=6170\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are actually three types of equations to solve:\r<BR>\n" );
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document.write( "1.  When you solve for x and get one or more solutions this is called a \"conditional equation.\"  This what usually happens, like when you solve x +3=5, the answer is x=2. This type of equation is called a CONDITIONAL EQUATION.\r<BR>\n" );
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document.write( "2.  Sometimes when you solve for x, it so happens that all the x's subtract out, and a false statement results.  For example, x+3 = 5 + x.  If you subtract x from each side, you get 3=5, which is NOT possible.  Therefore, there is NO SOLUTION, and that is where the answer is sometimes written with the greek letter phi (the circle with a line through it!). This type of equation is called a CONTRADICTION.\r<BR>\n" );
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document.write( "3.  Sometimes when you solve for x, it so happens that all the x's subtract out, and a TRUE statement results.  For example, x +3 = 3+x.  If you subtract x from each side, you get 3=3, or maybe 0=0, which is ALWAYS TRUE.  It's true no matter what x is, so this means the solution is all REAL values of x.  This type of equation is called an IDENTITY.\r<BR>\n" );
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document.write( "In yur example, <BR>\n" );
document.write( "2(4x+1)-x=7x+2<BR>\n" );
document.write( "8x + 2 - x = 7x + 2<BR>\n" );
document.write( "7x + 2 = 7x + 2\r<BR>\n" );
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document.write( "Subtract 7x from each side, and you get 2=2, which is always true.  The solution is all real values, and this is called an IDENTITY.\r<BR>\n" );
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document.write( "R^2 at SCC </SPAN>\n" );
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