document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=698582>Question 698582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x-3.          X+2<BR>\n" );
document.write( "______ = ______<BR>\n" );
document.write( " 5.                  6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #431045 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=431045\">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=%282x-3%29%2F5=%28x%2B2%29%2F6 ALIGN=MIDDLE  ALT=\"%282x-3%29%2F5=%28x%2B2%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The road to the solution of an equation may have several steps.<BR>\n" );
document.write( "In each step you change the equation into an equivalent equation, that has exactly the same solution(s), and is easier to solve.<BR>\n" );
document.write( "As for driving (or even walking) you have to look at the road far ahead to make sure that with each step you are going in the right direction.<BR>\n" );
document.write( "If you look at the ground just in front of you, you may zigzag, walk in the wrong direction, or even go around in circles.<BR>\n" );
document.write( "I'll show you what steps I would take, and you can decide if each step makes the equation easier to solve.<BR>\n" );
document.write( "At the end, I will give you a general tip (note) about how I plan my steps.<BR>\n" );
document.write( " <BR>\n" );
document.write( "STEP 1 - Get rid of denominators (usually a good first step).<BR>\n" );
document.write( "If you multiply both sides of the equal sign times the same (non-zero) number,<BR>\n" );
document.write( "you get an equivalent equation, that has exactly the same solution(s).<BR>\n" );
document.write( "Multiplying times 5 would get rid of the denominator on the left side.<BR>\n" );
document.write( "Multiplying times 6 would get rid of the denominator on the right side.<BR>\n" );
document.write( "We can do both at the same time by multiplying times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A6=30 ALIGN=MIDDLE  ALT=\"5%2A6=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Most people would write it as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30 ALIGN=MIDDLE  ALT=\"30\"   DISABLED_style= \"max-width:90%; height:auto;\" > , but I see it more clearly if I write it as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A6 ALIGN=MIDDLE  ALT=\"5%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A6%2A%28%282x-3%29%2F5%29=5%2A6%2A%28%28x%2B2%29%2F6%29 ALIGN=MIDDLE  ALT=\"5%2A6%2A%28%282x-3%29%2F5%29=5%2A6%2A%28%28x%2B2%29%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A6%2A%282x-3%29%2F5=5%2A6%2A%28x%2B2%29%2F6 ALIGN=MIDDLE  ALT=\"5%2A6%2A%282x-3%29%2F5=5%2A6%2A%28x%2B2%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%282x-3%29=5%28x%2B2%29 ALIGN=MIDDLE  ALT=\"6%282x-3%29=5%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x-18=5x%2B10 ALIGN=MIDDLE  ALT=\"12x-18=5x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "You probably have no problem solving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x-18=5x%2B10 ALIGN=MIDDLE  ALT=\"12x-18=5x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > , but I'll show how I would solve it.<BR>\n" );
document.write( " <BR>\n" );
document.write( "STEP 2<BR>\n" );
document.write( "If you add the same expression to both sides of an equation,<BR>\n" );
document.write( "you get an equivalent equation, that has exactly the same solution(s).<BR>\n" );
document.write( "I would add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18-5x ALIGN=MIDDLE  ALT=\"18-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x-18%2B18-5x=5x%2B10%2B18-5x ALIGN=MIDDLE  ALT=\"12x-18%2B18-5x=5x%2B10%2B18-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x-5x=10%2B18 ALIGN=MIDDLE  ALT=\"12x-5x=10%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x=28 ALIGN=MIDDLE  ALT=\"7x=28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "NOTES:<BR>\n" );
document.write( "Your teacher may think that you should do that in two steps (done in any order),<BR>\n" );
document.write( "adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18 ALIGN=MIDDLE  ALT=\"18\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides in one step, and<BR>\n" );
document.write( "subtracting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x ALIGN=MIDDLE  ALT=\"5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides in the other step.<BR>\n" );
document.write( "Going from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x-5x ALIGN=MIDDLE  ALT=\"12x-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x ALIGN=MIDDLE  ALT=\"7x\"   DISABLED_style= \"max-width:90%; height:auto;\" > sound as natural as 12 apples minus 5 apples = 7 apples,<BR>\n" );
document.write( "but your teacher may say that you have to show that you are \"taking out the common factor x\",<BR>\n" );
document.write( "or that you are applying the distributive property.<BR>\n" );
document.write( "Then you would have to write<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x-5x=10%2B18 ALIGN=MIDDLE  ALT=\"12x-5x=10%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812-5%29x=28 ALIGN=MIDDLE  ALT=\"%2812-5%29x=28\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x=28 ALIGN=MIDDLE  ALT=\"7x=28\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Whatever your teacher wants, it is wise to humor him or her.<BR>\n" );
document.write( " <BR>\n" );
document.write( "STEP 3<BR>\n" );
document.write( "If you divide both sides of the equal sign by the same (non-zero) number,<BR>\n" );
document.write( "you get an equivalent equation, that has exactly the same solution(s).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x=28 ALIGN=MIDDLE  ALT=\"7x=28\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2F7=28%2F7 ALIGN=MIDDLE  ALT=\"7x%2F7=28%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=4%29 ALIGN=MIDDLE  ALT=\"highlight%28x=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "A GENERAL NOTE:<BR>\n" );
document.write( "When solving simple (beginning algebra) equations,<BR>\n" );
document.write( "I try to \"undo\" all the \"processing\" done to the x in the expressions involved.<BR>\n" );
document.write( "That \"processing\" was done in a certain order, according to the \"order of operations\" rules.<BR>\n" );
document.write( "When \"undoing\" it, I must do it in reverse order.<BR>\n" );
document.write( "It just like taking off my shoes before taking off my socks when I undress,<BR>\n" );
document.write( "because I put my socks on before putting my shoes on when I dressed.<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "In <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2=29 ALIGN=MIDDLE  ALT=\"3x%2B2=29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the variable <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is first multiplied by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and after that, 2 is added.<BR>\n" );
document.write( "My first step must undo the adding of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2=29 ALIGN=MIDDLE  ALT=\"3x%2B2=29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2-2=29-2 ALIGN=MIDDLE  ALT=\"3x%2B2-2=29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=27 ALIGN=MIDDLE  ALT=\"3x=27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The next step is undoing the times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiplication:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=27 ALIGN=MIDDLE  ALT=\"3x=27\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2F3=27%2F3 ALIGN=MIDDLE  ALT=\"3x%2F3=27%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9 ALIGN=MIDDLE  ALT=\"x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );