document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203662>Question 203662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a hard time with Algebra.  Here's one I do not get. I do not get what the letters stand for.  Please help.....\r<BR>\n" );
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document.write( "Solve for w: 3w - 10 = 4w +5<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153670 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=153670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve for w: 3w - 10 = 4w +5\r<BR>\n" );
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document.write( "Hi.... don't get nervous.  This is all doable.   The letters in an equation are called \"Variables.\"  \r<BR>\n" );
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document.write( "Here's what I mean.   In your equation, 3w - 10 = 4w +5, we will find whatever number \"w\" will be, so that when we are all done, the side on the left side of the equal sign will equal the same thing on the right side of the equal sign.\r<BR>\n" );
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document.write( "To solve this problem, here's what I would tell you to do.  Try to get your \"w\" information on the left side of the equal sign and try to get your numbers on the right side of the equal sign.  \r<BR>\n" );
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document.write( "SO, let's look -- Here's your equation:  <BR>\n" );
document.write( "3w - 10 = 4w +5\r<BR>\n" );
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document.write( "Do you see that you have a 4w on the right side?   Well, it is a POSITIVE 4w, so what would happen, if you were to subtract 4w from that side of the equation?  \r<BR>\n" );
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document.write( "Before you do that tho, you have to know that in math, everything always has to be equal.  There must be a balance.  SOooo, if you subtract 4w from the RIGHT side, you have to \"be fair\" or \"make it balanced\" by subtracting 4w from the left side.  So, you'd have this:\r<BR>\n" );
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document.write( "3w - 10 - 4w = 4w +5 -4w (subtract 4w from the right side:  4w - 4w = 0)<BR>\n" );
document.write( "3w - 4w - 10 = 5  (see how we are now left with 5 on the right side?)<BR>\n" );
document.write( "-1w - 10 = 5  (Now, we have -1w - 10 on the left. Where did that -1w come from?  Well, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3w+-+4w+=+-1w ALIGN=MIDDLE  ALT=\"3w+-+4w+=+-1w\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have your \"w\" on the left but we have to get all the numbers on the right side.  So, on the left side we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1w+-+10 ALIGN=MIDDLE  ALT=\"-1w+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   There is a -10 there, so what if we ADD +10 to the left side.  AND, because we have to provide balance, then we have to ADD +10 on the right side too.  So, now we have:\r<BR>\n" );
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document.write( "-1w - 10 + 10 = 5 + 10   (See our +10 on both sides of the equal sign?)<BR>\n" );
document.write( "-1w = 15  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10+%2B+10+=+0 ALIGN=MIDDLE  ALT=\"-10+%2B+10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Therefore, we are left with -1w on the left side and of course 15 on the right.\r<BR>\n" );
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document.write( "Now what?  Well, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1w+=+15 ALIGN=MIDDLE  ALT=\"-1w+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > as our equation but we are still not done.  The \"w\" is not by itself.  When you want to isolate a variable, you have to ask yourself:  \"What is \"keeping company\" (so to speak) with the variable?\"  In this case, there is the -1 that is associated with the \"w\" and when there is no sign between a letter and a number, then you know you are multiplying.  \r<BR>\n" );
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document.write( "So -1 is being multiplied by \"w\".  \r<BR>\n" );
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document.write( "To sort of \"get rid of\" a number (in this case, the -1), we have to \"un do\" whatever is going on.  Because we are multiplying the way to \"un do\" multiplication is to do the opposite of what is going on.   What is the opposite of multiplying?  The answer is DIVIDING.\r<BR>\n" );
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document.write( "SO, let's divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1w%29%2F-1 ALIGN=MIDDLE  ALT=\"%28-1w%29%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND because we did that on the left, we have to do this on the right, so we have to say:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F-1 ALIGN=MIDDLE  ALT=\"15%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remember in grade school math that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F4 ALIGN=MIDDLE  ALT=\"4%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 1?  Well you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1w%29%2F-1 ALIGN=MIDDLE  ALT=\"%28-1w%29%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > just becomes 1, so you have 1w, or just plain 'ol w on the left.\r<BR>\n" );
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document.write( "On the right, you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F-1 ALIGN=MIDDLE  ALT=\"15%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   You are dividing a positive divided by a negative, so you get a negative.  SO your <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F-1+=+-15 ALIGN=MIDDLE  ALT=\"15%2F-1+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "That means w = -15.\r<BR>\n" );
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document.write( "Let's check to see if we are right........\r<BR>\n" );
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document.write( "Here is your original equation\r<BR>\n" );
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document.write( "3w - 10 = 4w +5<BR>\n" );
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document.write( "Any place you see a \"w\", I am going to \"plug in\" the number -15.  Here goes:\r<BR>\n" );
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document.write( "3w - 10 = 4w +5<BR>\n" );
document.write( "3(-15) - 10 = 4(-15) + 5   Let's do the math.  The number 3 times -15 = -45<BR>\n" );
document.write( "-45 - 10 = 4(-15) + 5  Let's do more math.  -45 - 10 is the same as: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-45+%2B+-10 ALIGN=MIDDLE  ALT=\"-45+%2B+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is -55.\r<BR>\n" );
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document.write( "-55 = 4(-15) + 5<BR>\n" );
document.write( "-55 = - 60 + 5<BR>\n" );
document.write( "-55 = -55\r<BR>\n" );
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document.write( "Now we have checked our answer and we know for sure that \"w\" equals -15, because when we put -15 into the original equation, both sides of the equal sign were........well...... EQUAL.  \r<BR>\n" );
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document.write( "Does this help?  I hope so...... </SPAN>\n" );
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