document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91996>Question 91996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> /3x+2/= 14<BR>\n" );
document.write( "/   / means absolute value<BR>\n" );
document.write( "This problem has either 2 solutions or \"no solutions\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66822 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=66822\">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%2B2%29+=+14 ALIGN=MIDDLE  ALT=\"abs%283x%2B2%29+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You are to solve for x.  A way to do this is to take the quantity inside the absolute<BR>\n" );
document.write( "value signs and precede it with plus and minus signs and solve it like an equation.<BR>\n" );
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document.write( "In other words, the quantity inside the absolute value signs is (3x + 2).  So you set up two<BR>\n" );
document.write( "equations ... one using +(3x+2) and the other using -(3x+2).<BR>\n" );
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document.write( "The first equation is:<BR>\n" );
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document.write( "+(3x +2) = 14<BR>\n" );
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document.write( "Since the parentheses are preceded by a plus sign, you can just remove them to get:<BR>\n" );
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document.write( "3x + 2 = 14<BR>\n" );
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document.write( "Get rid of the 2 on the left side by subtracting 2 from both sides to get:<BR>\n" );
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document.write( "3x = 12<BR>\n" );
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document.write( "Solve for x by dividing both sides by 3 and you get:<BR>\n" );
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document.write( "x = 12/3 = 4<BR>\n" );
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document.write( "So x = 4 is one of the answers.<BR>\n" );
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document.write( "Now set up a second equation using minus the quantity inside the absolute value signs. This<BR>\n" );
document.write( "equation becomes:<BR>\n" );
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document.write( "-(3x + 2) = 14<BR>\n" );
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document.write( "The minus sign in front of the parentheses tells you to change the sign of every term in<BR>\n" );
document.write( "the parentheses if you wish to remove the parentheses. Therefore, when you remove the<BR>\n" );
document.write( "parentheses this equation becomes:<BR>\n" );
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document.write( "-3x - 2 = 14<BR>\n" );
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document.write( "Get rid of the -2 on the left side by adding 2 to both sides.  When you do the equation<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "-3x = 16<BR>\n" );
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document.write( "Now solve for x by dividing both sides by -3. This division makes the equation become:<BR>\n" );
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document.write( "x = -16/3<BR>\n" );
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document.write( "So now you have the two answers: x = 4 and x = -16/3<BR>\n" );
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document.write( "Let's check them out. The original equation was:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283x+%2B2%29+=+14 ALIGN=MIDDLE  ALT=\"abs%283x+%2B2%29+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Setting x equal to 4 results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%283%2A4%29%2B2%29+=+14 ALIGN=MIDDLE  ALT=\"abs%28%283%2A4%29%2B2%29+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiplying inside the absolute value signs gives:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%2812%29%2B2%29+=+14 ALIGN=MIDDLE  ALT=\"abs%28%2812%29%2B2%29+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%2814%29+=+14 ALIGN=MIDDLE  ALT=\"abs%2814%29+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And since the absolute value of +14 is 14, this equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14+=+14 ALIGN=MIDDLE  ALT=\"14+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which is true. Therefore, x = 4 is a good solution.<BR>\n" );
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document.write( "Next let's check out the other answer x = -16/3.<BR>\n" );
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document.write( "Begin with<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283x+%2B2%29+=+14 ALIGN=MIDDLE  ALT=\"abs%283x+%2B2%29+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute -16/3 for x and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%283%2A%28-16%2F3%29%29+%2B2%29+=+14 ALIGN=MIDDLE  ALT=\"abs%28%283%2A%28-16%2F3%29%29+%2B2%29+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Doing the multiplication inside the absolute value signs gives:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%28-48%2F3%29+%2B+2%29+=+14 ALIGN=MIDDLE  ALT=\"abs%28%28-48%2F3%29+%2B+2%29+=+14\"   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=-48%2F3+=+-16 ALIGN=MIDDLE  ALT=\"-48%2F3+=+-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > the equation simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-16%2B2%29+=+14 ALIGN=MIDDLE  ALT=\"abs%28-16%2B2%29+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The addition inside the absolute value signs results in -14 so the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-14%29+=+14 ALIGN=MIDDLE  ALT=\"abs%28-14%29+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "but the absolute value of -14 is 14, so the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14+=+14 ALIGN=MIDDLE  ALT=\"14+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and since this is true, the answer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-16%2F3 ALIGN=MIDDLE  ALT=\"x+=+-16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is also correct.<BR>\n" );
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document.write( "Hope this shows you a way to solve absolute value equations of this type. Just take the<BR>\n" );
document.write( "plus and minus quantities of the expression inside the absolute value signs and set up<BR>\n" );
document.write( "two equations.  Then solve them just as you would an ordinary equation. This will give<BR>\n" );
document.write( "you the answers. And it is a good practice to check your answers as was done above.<BR>\n" );
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document.write( " </SPAN>\n" );
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