document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186160>Question 1186160</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the manufacture of​ widgets, the average dimension of a part is 0.005 cm. Using the​ absolute-value symbol, express the fact that an individual measurement x of a part does not differ from the average by more than 0.0006 cm. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #817039 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=817039\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe the equation is going to be:\r<BR>\n" );
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document.write( "abs(x - .005) <= .0006\r<BR>\n" );
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document.write( "the absolute value property of an equation is such that:\r<BR>\n" );
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document.write( "if the expression inside the absolute value sign is positive, then the inequality becomes:\r<BR>\n" );
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document.write( "(x - .005) <= .0006\r<BR>\n" );
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document.write( "if the expression inside the absolute value sign is negative, then the inequality becomes:\r<BR>\n" );
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document.write( "-(x - .005) <= .0006\r<BR>\n" );
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document.write( "we'll solve for when the expression inside the absolute value sign is positive.\r<BR>\n" );
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document.write( "(x - .005) <= .0006\r<BR>\n" );
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document.write( "remove the parentheses to get:\r<BR>\n" );
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document.write( "x - .005 <= .0006\r<BR>\n" );
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document.write( "add .005 to both sides of the inequality to get:\r<BR>\n" );
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document.write( "x <= .0006 + .005\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x <= .0056\r<BR>\n" );
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document.write( "now we'll solve for when the expression within the absolute value sign is negative.\r<BR>\n" );
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document.write( "-(x - .005) <= .0006\r<BR>\n" );
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document.write( "multiply both sides of this inequality by -1 to get:\r<BR>\n" );
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document.write( "(x - .005) >= -.0006\r<BR>\n" );
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document.write( "multiplying both sides of an inequality by a negative number reverses the inequality.\r<BR>\n" );
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document.write( "that's why the inequality is now >= rather than <=.\r<BR>\n" );
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document.write( "remove the parentheses to get:\r<BR>\n" );
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document.write( "x - .005 >= -.0006\r<BR>\n" );
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document.write( "add .005 to both sides of the inequality to get:\r<BR>\n" );
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document.write( "x >= -.0006 + .005\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x >= .0044\r<BR>\n" );
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document.write( "your solution is that the absolute value inequality is:\r<BR>\n" );
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document.write( "|x - .005| <= .0006\r<BR>\n" );
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document.write( "this leads to the value of x being greater than .0044 and less than .0056, which can be expressed as:\r<BR>\n" );
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document.write( ".0044 <= x <= .0056\r<BR>\n" );
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document.write( " </SPAN>\n" );
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