document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=729598>Question 729598</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what does -x+1x equal?<BR>\n" );
document.write( "I am trying to solve an equation with this in it....just trying to combine like terms thats all </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #446045 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=446045\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x=x ALIGN=MIDDLE  ALT=\"1x=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1x=-x ALIGN=MIDDLE  ALT=\"-1x=-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We do not usually take the trouble to write the 1 and -1 in front of x as visible coefficients.<BR>\n" );
document.write( "You could think of it as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B1x=-1x%2B1x=%28-1%2B1%29x=0%2Ax=0 ALIGN=MIDDLE  ALT=\"-x%2B1x=-1x%2B1x=%28-1%2B1%29x=0%2Ax=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Maybe you could just write<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B1x=-x%2Bx=0 ALIGN=MIDDLE  ALT=\"-x%2B1x=-x%2Bx=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or even shorter as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B1x=-x%2Bx=0 ALIGN=MIDDLE  ALT=\"-x%2B1x=-x%2Bx=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The question is how much writing does your teacher expect.<BR>\n" );
document.write( "Are you expected to write more baby steps that seems obvious to me and your teacher just to show that you understand what you are doing?<BR>\n" );
document.write( "Or would the extra steps just seem ridiculous and annoying to your teacher?<BR>\n" );
document.write( "If you had more than a couple of weeks of algebra classes, I would not want to see extra steps.<BR>\n" );
document.write( " <BR>\n" );
document.write( "MY UNDERSTANDING OF ALGEBRA:<BR>\n" );
document.write( "Subtraction does not really exist. It is just a reflection of addition, just like the trees you see inside the water on a still pond are just the reflection of trees on the ground next to the pond.<BR>\n" );
document.write( "A negative number means just go in the other direction.<BR>\n" );
document.write( "5-3 is really 5 + (-3) , which could mean go miles North and them go 3 miles South.<BR>\n" );
document.write( "Each variable has a coefficient (a number in front of the variable) even if you do not see one.<BR>\n" );
document.write( "x-3x means really 1x + (-3)x, which could mean 1 mile North, then 3 miles South, or one small step North, then 3 small steps South, or deposit one dollar in the bank account, then withdraw 3 dollars. It does not matter what x means, I can add up all the x together.<BR>\n" );
document.write( "I do not write more than needed, it just write x-3x=-2x, although I understand that x is 1 times x, -3x is (-3) times x, and they are added so I get (-2) times x.<BR>\n" );
document.write( "If you ever see a minus sign in front of a parenthesis, as in<BR>\n" );
document.write( "2(x-5)-(x+2) try to see an invisible 1.<BR>\n" );
document.write( "It is really 2(x + (-5)) + (-1)(x + 2)= 2x + 2(-5) + (-1)x + (-1)2 = 2x + (-10) + (-1)x + (-2) <BR>\n" );
document.write( "The result is 2x + (-10) + (-1)x + (-2), which I write as 2x-10-x-2 .<BR>\n" );
document.write( "Next I collect like terms, understanding that what I am doing is rearranging the pieces I am adding and that in baby steps is<BR>\n" );
document.write( "2x + (-10) + (-1)x + (-2) = (2x + (-1)x) + ((-10) + (-2)) = (2 + (-1))x + (-12) = 1x + (-12)<BR>\n" );
document.write( "I write that final result as just x-12.<BR>\n" );
document.write( "I write the whole calculation as<BR>\n" );
document.write( "2(x-5)-(x+2) = 2x-10-x-2 = x-12 ,<BR>\n" );
document.write( "but I understand that I am working with adding and multiplying positive and negative numbers, some of which are multiplied times x, and since no one has given me a value for x, I have to keep the x stuff separated from the stuff that does not have x (as if it were in separate accounts). </SPAN>\n" );
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