document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164498>Question 1164498</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (i)Use the definition of absolute value to solve each equation,<BR>\n" );
document.write( "ii) Graph the solution<BR>\n" );
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document.write( "|-1/5 - 1/2k| = 9/5<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 #789021 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> definition of absolute value.\r<BR>\n" );
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document.write( "absolute value of x if x is positive and absolute value of x is -x if x is negative.\r<BR>\n" );
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document.write( "the absolute value of an expression is always positive.\r<BR>\n" );
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document.write( "your problem states that |-1/5 - 1/2 * k| = 9/5\r<BR>\n" );
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document.write( "by the definition, when the expression is positive it is equal to 9/5 and when the expression is negative, then minus the expression is equal to 9/5.\r<BR>\n" );
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document.write( "therefore:\r<BR>\n" );
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document.write( "when the expression is positive, you get:\r<BR>\n" );
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document.write( "(-1/5 - 1/2 * k) = 9/5<BR>\n" );
document.write( "this becomes -1/5 - 1/2 * k = 9/5<BR>\n" );
document.write( "add 1/5 to both sides of the equation and simplify to get:<BR>\n" );
document.write( "-1/2 * k = 10/5<BR>\n" );
document.write( "solve for k to get:<BR>\n" );
document.write( "k = -20/5 = -4<BR>\n" );
document.write( "confirm by replacing k in the original equation to get:<BR>\n" );
document.write( "|-1/5 - 1/2 * k| = 9/5<BR>\n" );
document.write( "this becomes |9/5| = 9/5 which becomes 9/5 = 9/5, confirming the value of k is correct.\r<BR>\n" );
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document.write( "when the expression is negative, you get:\r<BR>\n" );
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document.write( "-(-1/5 - 1/2 * k) = 9/5<BR>\n" );
document.write( "this becomes 1/5 + 1/2 * k = 9/5<BR>\n" );
document.write( "subtract 1/5 from both sides of the equation and simplify to get:<BR>\n" );
document.write( "1/2 * k = 8/5<BR>\n" );
document.write( "solve for k to get:<BR>\n" );
document.write( "k = 16/5 = 3.2<BR>\n" );
document.write( "confirm by replacing k in the original equation to get:<BR>\n" );
document.write( "|-1/5 - 1/2 * 16/5| = 9/5 which becomes |-1/5 - 8/5| = 9/5 which becomes |-9/5| = 9/5 which becomes 9/5 = 9/5, confirming the value of k is good.\r<BR>\n" );
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document.write( "you can graph two equations as shown below:\r<BR>\n" );
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document.write( "y = |-1/5 - 1/2 * x| and y = 9/5\r<BR>\n" );
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document.write( "the intersection of the two equations is the solution.<BR>\n" );
document.write( "that solution is x = -4 and x = 3.2<BR>\n" );
document.write( "x = 3.2 is the same as x = 16/5.\r<BR>\n" );
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document.write( "you can also graph one equation as shown below:\r<BR>\n" );
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document.write( "y - |-1/5 - 1/2 * x| - y = 9/5<BR>\n" );
document.write( "the intersection of the equation with the x-axis is the solution.\r<BR>\n" );
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document.write( "the graph of both solutions is shown below:\r<BR>\n" );
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document.write( "you can see that the x-coordinate of both graphs are the same.<BR>\n" );
document.write( "those are your solutions.<BR>\n" );
document.write( "the y-coordinates will be different because the second graph is shifted down 9/5 units of y.\r<BR>\n" );
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document.write( "y = 9/5 is the same as y = 1.8.\r<BR>\n" );
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