document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=97639>Question 97639</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear Tutor/or Tutors,<BR>\n" );
document.write( "I would greatly appreciate it if you can help me solve the following problem and let me know how you did so;\r<BR>\n" );
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document.write( "5 more than two thirds of the number is the same as 3 less than one half of the number.\r<BR>\n" );
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document.write( "Thank You Very Much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #71042 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=71042\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The number you are looking for is unknown. So call it x.<BR>\n" );
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document.write( "Two-thirds of the number is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29x ALIGN=MIDDLE  ALT=\"%282%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and 5 more than that is written as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29x+%2B+5 ALIGN=MIDDLE  ALT=\"%282%2F3%29x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=== left side of the equation we are working toward<BR>\n" );
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document.write( "That is the same (meaning equal to) 3 less than one-half the number. One-half the number is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29x ALIGN=MIDDLE  ALT=\"%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and 3 less than that is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29x+-+3 ALIGN=MIDDLE  ALT=\"%281%2F2%29x+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=== right side of the equation we are getting<BR>\n" );
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document.write( "So now we have two sides that are to be equal. In equation form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29x+%2B+5+=+%281%2F2%29x+-+3 ALIGN=MIDDLE  ALT=\"%282%2F3%29x+%2B+5+=+%281%2F2%29x+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let's get rid of the fractions by multiplying both sides of this equation (all terms) by <BR>\n" );
document.write( "a common denominator of 6. (Note that we get 6 by multiplying the two denominators of<BR>\n" );
document.write( "3 and 2). Multiplying both sides of the equation (all terms) by 6 results in the equation<BR>\n" );
document.write( "becoming:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2812%2F3%29x+%2B+30+=+%286%2F2%29x+-+18 ALIGN=MIDDLE  ALT=\"+%2812%2F3%29x+%2B+30+=+%286%2F2%29x+-+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Doing the division in the two sets of parentheses simplifies the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2B+30+=+3x+-+18 ALIGN=MIDDLE  ALT=\"4x+%2B+30+=+3x+-+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the 3x on the right side by subtracting 3x from both sides. When you do that<BR>\n" );
document.write( "the equation reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+30+=+-+18 ALIGN=MIDDLE  ALT=\"x+%2B+30+=+-+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now get rid of +30 on the left side by subtracting 30 from both sides to end up with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-48 ALIGN=MIDDLE  ALT=\"x+=+-48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That's the answer. Let's check it by using it in the original problem statement.<BR>\n" );
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document.write( "One-third of -48 is -16. So two-thirds of -48 is -32. 5 more than -32 is - 27 (-32 + 5 = -27).<BR>\n" );
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document.write( "That is to be equal to 3 less than one-half the number.  One-half of -48 is - 24 and if you take<BR>\n" );
document.write( "away 3 from -24 you have (-24 - 3) -27.  So the answer of -27 works because it makes both<BR>\n" );
document.write( "sides of the equation equal to -27.<BR>\n" );
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document.write( "Hope this helps you to understand this problem.  Getting rid of the fractions is a technique<BR>\n" );
document.write( "that often saves you from the complexity of multiplying, dividing, adding, and subtracting <BR>\n" );
document.write( "in fractional form. Hope that helps.<BR>\n" );
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