document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122951>Question 1122951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A poll found that a particular group of people read an average of 12.3 books per year. The pollsters are&#8203; 99% confident that the result from this poll is off by fewer than 2.74 books from the actual average x. Express this situation as an inequality involving absolute&#8203; value, and solve the inequality for x to determine the interval in which the average is likely to fall.Express the situation as an inequality involving absolute value </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739164 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=739164\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the average is 12.3 booke per year.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the pollsters are 99% confident that the actual results will not be off by more than 2.74 books plus or minus.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that means the actual results can be as little as 12.3 minus 2.74 or as much as 12.3 plus 2.74.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if x is the amount that the actual results can be off, then you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x - 12.3 < 2.75 or x - 12.3 > -2.75\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this can be written as -2.75 < x - 12.3 < 2.75\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this leads to the absolute value expression that says |x - 12.3| < 2.75\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this absolute value expression is interpreted as:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when (x - 12.3) is positive, the expression becomes (x - 12.3) < 2.75\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when (x - 12.3) is negative, the expression becomes (x - 12.3) > - 2.75\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when you combine these two expressions together, you get -2.75 < (x - 12.3) < 2.75.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for example, let's' assume that the actual value is 2.5 units off the average.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "then the actual value will be between 12.3 - 2.5 and 12.3 + 2.5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this makes the actual value between 9.8 and 14.8.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the actual value is 14.8, then the expression |14.8 - 12.3| < 2.75 becomes |2.5| < 2.75, which is true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the actual value is 9.8, then the expression |9.8 - 12.3| < 2.75 becomes |-2.5| < 2.75, which is also true, since |-2.5| is equal to 2.5 and that is smaller than 2.75.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a reference on absolute value expressions you might find helpful.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "$$$$$\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "note that the strict definition of absolute value expressions is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if A is positive, then |A| = A.<BR>\n" );
document.write( "if A is negative, then |A| = -A.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this leads to:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if |A| < B, and A is positive, then A < B.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if |A| < B, and A is negative, then -A < B.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the expression -A < B, if you multiply both sides of the expression by -1, you get A > -B.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that leads to:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if |A| < B, and A is positive, then A < B.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if |A| < B, and A is negative, then A > -B.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "both A and B represent expressions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in your example of:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "|x - 12.3| < 2.75\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x - 12.3) would be the expression shown as A.<BR>\n" );
document.write( "2.75 would be the expression shown as B.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's some references on absolute value expressions you might find helpful.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.basic-mathematics.com/definition-of-absolute-value.html\" target = \"_blank\">https://www.basic-mathematics.com/definition-of-absolute-value.html</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.purplemath.com/modules/absineq.htm\" target = \"_blank\">https://www.purplemath.com/modules/absineq.htm</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.umsl.edu/~defreeseca/intalg/ch2extra/absineq.htm\" target = \"_blank\">http://www.umsl.edu/~defreeseca/intalg/ch2extra/absineq.htm</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );