document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=458473>Question 458473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i need help with my - and + signs what are the rules </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #314528 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=314528\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rule 1:\r<BR>\n" );
document.write( "\n" );
document.write( "Addition of  two Numbers with the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=same ALIGN=MIDDLE  ALT=\"same\"   DISABLED_style= \"max-width:90%; height:auto;\" > sign\r<BR>\n" );
document.write( "\n" );
document.write( " The result is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum ALIGN=MIDDLE  ALT=\"sum\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the numbers with the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=given ALIGN=MIDDLE  ALT=\"given\"   DISABLED_style= \"max-width:90%; height:auto;\" > sign ( the sign of the two numbers )  .\r<BR>\n" );
document.write( "\n" );
document.write( " When we add two  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=plus ALIGN=MIDDLE  ALT=\"plus\"   DISABLED_style= \"max-width:90%; height:auto;\" > numbers we get a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=plus ALIGN=MIDDLE  ALT=\"plus\"   DISABLED_style= \"max-width:90%; height:auto;\" > number.   Example :  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2B6=9 ALIGN=MIDDLE  ALT=\"+3%2B6=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "\n" );
document.write( " When we add two <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=minus ALIGN=MIDDLE  ALT=\"minus\"   DISABLED_style= \"max-width:90%; height:auto;\" > numbers we get a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=minus ALIGN=MIDDLE  ALT=\"minus\"   DISABLED_style= \"max-width:90%; height:auto;\" > number.   Example:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+%2B+%28-+6+%29=+-+11 ALIGN=MIDDLE  ALT=\"-5+%2B+%28-+6+%29=+-+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
document.write( "\n" );
document.write( "Rule 2 :  \r<BR>\n" );
document.write( "\n" );
document.write( "Addition of two numbers with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=different ALIGN=MIDDLE  ALT=\"different\"   DISABLED_style= \"max-width:90%; height:auto;\" > signs  the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=result ALIGN=MIDDLE  ALT=\"result\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=difference ALIGN=MIDDLE  ALT=\"difference\"   DISABLED_style= \"max-width:90%; height:auto;\" > between the numbers with the sign of the\" <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=bigger ALIGN=MIDDLE  ALT=\"bigger\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+number ALIGN=MIDDLE  ALT=\"+number\"   DISABLED_style= \"max-width:90%; height:auto;\" > \" .\r<BR>\n" );
document.write( "\n" );
document.write( "  Example:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+%2B+%28-+9+%29=+-+3 ALIGN=MIDDLE  ALT=\"6+%2B+%28-+9+%29=+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Rule 3 : \r<BR>\n" );
document.write( "\n" );
document.write( "Multiplication and signs :\r<BR>\n" );
document.write( "\n" );
document.write( "  The basic rules for multiplication and signs  are as follows\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28Minus+%29%28+Minus+%29+=++Plus ALIGN=MIDDLE  ALT=\"%28Minus+%29%28+Minus+%29+=++Plus\"   DISABLED_style= \"max-width:90%; height:auto;\" >    \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+Minus+%29+%28+Plus+%29++=+Minus ALIGN=MIDDLE  ALT=\"%28+Minus+%29+%28+Plus+%29++=+Minus\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28Plus+%29+%28Plus+%29++=++Plus+ ALIGN=MIDDLE  ALT=\"%28Plus+%29+%28Plus+%29++=++Plus+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This can be expressed as follows that \r<BR>\n" );
document.write( "\n" );
document.write( "(a) when we multiply two  numbers with the same sign   we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=plus+ ALIGN=MIDDLE  ALT=\"plus+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( " ( b) when we multiply  two numbers with difference signs  we get a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=minus ALIGN=MIDDLE  ALT=\"minus\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Example : \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-+7%29+%2A+%28-+5%29+=++35 ALIGN=MIDDLE  ALT=\"+%28-+7%29+%2A+%28-+5%29+=++35\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-7+%29%2A+5++=+-35 ALIGN=MIDDLE  ALT=\"%28-7+%29%2A+5++=+-35\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Rule 4 :  Letters\r<BR>\n" );
document.write( "\n" );
document.write( "Letters are often used in place of numbers , letters are often referred to  as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=variables ALIGN=MIDDLE  ALT=\"variables\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=unknowns ALIGN=MIDDLE  ALT=\"unknowns\"   DISABLED_style= \"max-width:90%; height:auto;\" > . \r<BR>\n" );
document.write( "\n" );
document.write( "Rules 1,2,3 above apply to all calculations with letters , we have to remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=one ALIGN=MIDDLE  ALT=\"one\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+further ALIGN=MIDDLE  ALT=\"+further\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+rule ALIGN=MIDDLE  ALT=\"+rule\"   DISABLED_style= \"max-width:90%; height:auto;\" > which applies to letters that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=we ALIGN=MIDDLE  ALT=\"we\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+can+ ALIGN=MIDDLE  ALT=\"+can+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=only+ ALIGN=MIDDLE  ALT=\"only+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=add ALIGN=MIDDLE  ALT=\"add\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+things ALIGN=MIDDLE  ALT=\"+things\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+together ALIGN=MIDDLE  ALT=\"+together\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+that+ ALIGN=MIDDLE  ALT=\"+that+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=are+ ALIGN=MIDDLE  ALT=\"are+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=the ALIGN=MIDDLE  ALT=\"the\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+same+ ALIGN=MIDDLE  ALT=\"+same+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, in other words we can only add x's to x's and y's to y's etc  .  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Example \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a+-+7a+=+-+2a ALIGN=MIDDLE  ALT=\"5a+-+7a+=+-+2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > ....Note also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a+ ALIGN=MIDDLE  ALT=\"5a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > times<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+ ALIGN=MIDDLE  ALT=\"a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "or\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-+3x+%2B++7x++=+4x ALIGN=MIDDLE  ALT=\"+-+3x+%2B++7x++=+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >}\r<BR>\n" );
document.write( "\n" );
document.write( "or\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5a+%2B+6b+-+4a+-+11b+%2C=+5a+-+4a++%2B+6b+-+11b+=++a+-+5b+ ALIGN=MIDDLE  ALT=\"+5a+%2B+6b+-+4a+-+11b+%2C=+5a+-+4a++%2B+6b+-+11b+=++a+-+5b+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Rule 5 :    Brackets \r<BR>\n" );
document.write( "\n" );
document.write( "(a) A number immediately outside a bracket means that everything inside the bracket gets multiplied by that number   \r<BR>\n" );
document.write( "\n" );
document.write( "Ex.: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%285%29=4%2A5=20 ALIGN=MIDDLE  ALT=\"4%285%29=4%2A5=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "(b)Minus sign  outside a bracket will change all the signs inside the brackets when the brackets are removed : \r<BR>\n" );
document.write( "\n" );
document.write( "Ex.: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%285%29=-4%2A5=-20 ALIGN=MIDDLE  ALT=\"-4%285%29=-4%2A5=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "(c)Minus number outside a bracket does two things \r<BR>\n" );
document.write( "\n" );
document.write( "(1) everything inside the bracket gets multiplied by the number and \r<BR>\n" );
document.write( "\n" );
document.write( "(2) all the signs change\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%282x-3x%29=-2x%2B3x=x ALIGN=MIDDLE  ALT=\"-%282x-3x%29=-2x%2B3x=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Brackets by brackets :\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply everything in the second bracket by everything in the first bracket and tidy it up .\r<BR>\n" );
document.write( "\n" );
document.write( "Ex.:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%28x%2B1%29=x%5E2%2Bx-x%2B1%2A%28-1%29=x%5E2-1 ALIGN=MIDDLE  ALT=\"%28x-1%29%28x%2B1%29=x%5E2%2Bx-x%2B1%2A%28-1%29=x%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );