document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141453>Question 1141453</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The range of temperatures on a particular day could be described as |x—68| <= 9. How many integer values are included in the range? <BR>\n" );
document.write( "A) |x+4|<8<BR>\n" );
document.write( "B)|x—5|<3\r<BR>\n" );
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document.write( "Which integer value of x that satisfies both inequalities shown above? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762000 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13219)</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=762000\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "One way to solve absolute value problems like this is to interpret<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-a%29%3C=b ALIGN=MIDDLE  ALT=\"abs%28x-a%29%3C=b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "as meaning the difference between x and a is at most b.  So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-68%29%3C=9 ALIGN=MIDDLE  ALT=\"abs%28x-68%29%3C=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "means x is at most 9 away from 68.  68-9 = 59; 68+9 = 77.  The number of integers from 59 to 77 inclusive is (77-59)+1 = 19.<br><BR>\n" );
document.write( "A)  Using the same interpretation, x has to be less than 8 away from -4.  -4-8 = -12; -4+8 = 4.  Since this is a strict inequality, the integer solutions are from -11 to 3 inclusive, which is 15 values.<br><BR>\n" );
document.write( "B)  This one says x is less than 3 away from 5: from 3 to 7, which is 5 values.<br><BR>\n" );
document.write( "From these three problems, you should note that<br><BR>\n" );
document.write( "(1) the number of integer solutions to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-a%29%3C=b ALIGN=MIDDLE  ALT=\"abs%28x-a%29%3C=b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 2b+1; and<BR>\n" );
document.write( "(2) the number of integer solutions to<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-a%29%3Cb ALIGN=MIDDLE  ALT=\"abs%28x-a%29%3Cb\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 2b-1. </SPAN>\n" );
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