document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80743>Question 80743</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following is the solution set of \r<BR>\n" );
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document.write( "|3x+ 18|=12\r<BR>\n" );
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document.write( "A. (2) B. (2,10) C.(-10, -2) D.(10) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57934 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=57934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283x%2B18%29=12 ALIGN=MIDDLE  ALT=\"abs%283x%2B18%29=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "What is the solution set?<BR>\n" );
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document.write( "Work this as two separate problems.  For the first problem, replace the absolute value signs<BR>\n" );
document.write( "with parentheses that are preceded by a + sign.  For the second problem, replace the absolute<BR>\n" );
document.write( "value signs with parentheses that are preceded by a - sign. Let's do it.<BR>\n" );
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document.write( "First problem. Replacing the absolute value signs by parentheses preceded by a + sign results<BR>\n" );
document.write( "in:<BR>\n" );
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document.write( "+(3x + 18) = 12<BR>\n" );
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document.write( "Since the leading sign preceding the parentheses is + you can just remove the parentheses<BR>\n" );
document.write( "and you get:<BR>\n" );
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document.write( "3x + 18 = 12<BR>\n" );
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document.write( "Solve by subtracting 18 from both sides and you have:<BR>\n" );
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document.write( "3x = -6<BR>\n" );
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document.write( "Divide by 3 and you get:<BR>\n" );
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document.write( "x = -6/3 = -2<BR>\n" );
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document.write( "Second problem.  Replace the absolute value signs by parentheses preceded by a minus sign<BR>\n" );
document.write( "and you get:<BR>\n" );
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document.write( "-(3x + 18) = 12<BR>\n" );
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document.write( "This time when you remove the parentheses, the leading minus sign requires that you change<BR>\n" );
document.write( "the sign of all the terms inside the parentheses. When you remove the parentheses <BR>\n" );
document.write( "you get:<BR>\n" );
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document.write( "-3x - 18 = 12<BR>\n" );
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document.write( "Get rid of the - 18 on the left side by adding + 18 to both sides to get:<BR>\n" );
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document.write( "-3x = 30<BR>\n" );
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document.write( "Solve by dividing both sides by -3 and you get:<BR>\n" );
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document.write( "x = 30/(-3) = -10<BR>\n" );
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document.write( "Check your two answers by putting them into the given absolute value equation. First check<BR>\n" );
document.write( "the -2 answer.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283%2A%28-2%29%2B+18%29+=+12 ALIGN=MIDDLE  ALT=\"abs%283%2A%28-2%29%2B+18%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "the 3*(-2) equals -6 and substituting this -6 results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-6+%2B+18%29+=+12 ALIGN=MIDDLE  ALT=\"abs%28-6+%2B+18%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "combining the terms in the absolute value signs gives you:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%2812%29+=+12 ALIGN=MIDDLE  ALT=\"abs%2812%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "and since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%2812%29 ALIGN=MIDDLE  ALT=\"abs%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is +12, this equation works.<BR>\n" );
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document.write( "Next substitute -10 for x and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283%2A%28-10%29%2B18%29+=+12 ALIGN=MIDDLE  ALT=\"abs%283%2A%28-10%29%2B18%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Do the multiplication in the parentheses to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-30+%2B+18%29+=+12 ALIGN=MIDDLE  ALT=\"abs%28-30+%2B+18%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "combine the terms in the absolute value signs to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-12%29+=+12 ALIGN=MIDDLE  ALT=\"abs%28-12%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And the absolute value of -12 is +12 so the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+=+12 ALIGN=MIDDLE  ALT=\"12+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So this answer checks also.<BR>\n" );
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document.write( "Another way you could have considered doing this problem is to substitute each of the<BR>\n" );
document.write( "given answers into the original equation to see if it works. For example, Answer A is 2.<BR>\n" );
document.write( "Substitute 2 for x in the original problem and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283%2A2+%2B+18%29+=+12 ALIGN=MIDDLE  ALT=\"abs%283%2A2+%2B+18%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "this simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%286%2B18%29+=+12 ALIGN=MIDDLE  ALT=\"abs%286%2B18%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this further simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%2824%29+=+12 ALIGN=MIDDLE  ALT=\"abs%2824%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is obviously wrong so A cannot be the answer.  And if you do a similar process for<BR>\n" );
document.write( "answers B and D you will see they do not work either.  Sometimes on the ACT and SAT exams<BR>\n" );
document.write( "this method will save time.  Just check the answers until you find the one that works.<BR>\n" );
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document.write( "Hope this helps you to understand a method for doing absolute value problems.<BR>\n" );
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