document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155747>Question 1155747</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For each of the figures, write Absolute Value equation in the form <BR>\n" );
document.write( "|x−c|<BR>\n" );
document.write( "=d, where c and d are some numbers, to satisfy the given solution set.<BR>\n" );
document.write( "x=-1/2, x=1/2<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 #778396 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13332)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=778396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You want an absolute value equation in the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-c%29=d ALIGN=MIDDLE  ALT=\"abs%28x-c%29=d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "that has the solution set x=1/2 and x=-1/2.<br><BR>\n" );
document.write( "Interpret the equation as saying \"the difference between x and c is d\", allowing the difference to be either x-c or c-x.  On a number line, this is equivalent to saying that x and c are separated by a distance d.<br><BR>\n" );
document.write( "So for this particular problem, we are looking for numbers c and d for which both x=1/2 and x=-1/2 are the same distance d from c.<br><BR>\n" );
document.write( "If x=1/2 and x=-1/2 are the same distance d from c, then c has to be halfway between x=1/2 and x=-1/2; and the distance d is the distance from that c to either of the x values.<br><BR>\n" );
document.write( "Halfway between 1/2 and -1/2 is 0, so c is 0; and each of those x values is 1/2 unit from 0, so d is 1/2.<br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-0%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"abs%28x-0%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "It is easy to show that x=1/2 and x=-1/2 are the only two solutions to that equation.<br><BR>\n" );
document.write( "Let's look at a more interesting example, with the two solutions being x=5 and x=13.<br><BR>\n" );
document.write( "Halfway between 5 and 13 is 9; and the distance from 9 to either 5 or 13 is 4.  So the equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-9%29=4 ALIGN=MIDDLE  ALT=\"abs%28x-9%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That equation says the difference between x and 9 is 4; the two values for x are 9+4=13 and 9-4=5.<br><BR>\n" );
document.write( "Or...<br><BR>\n" );
document.write( "Solving that absolute value equation in the usual way, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-9=4 ALIGN=MIDDLE  ALT=\"x-9=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-9+=+-4 ALIGN=MIDDLE  ALT=\"x-9+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+13 ALIGN=MIDDLE  ALT=\"x+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5 ALIGN=MIDDLE  ALT=\"x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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