document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190443>Question 1190443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ashley estimates that there are a marbles in a jar. Harry, who knows the actual number of marbles in the jar, b, notes that Ashley’s estimate is within 15 marbles (inclusive) of the actual number of  marbles. Which of the following inequalities represents the relationship between Ashley’s estimate and the actual number of marbles in the jar?<BR>\n" );
document.write( "a) -15≤a-b≤15<BR>\n" );
document.write( "b) a≤b+15<BR>\n" );
document.write( "c) a≥b-15<BR>\n" );
document.write( "d) a+b≥15 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822067 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822067\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "a = Ashley's estimate<BR>\n" );
document.write( "b = true amount<BR>\n" );
document.write( "a-b = difference of the two items\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The difference represents how far off Ashley is. <BR>\n" );
document.write( "For example, if she guesses a= 10 marbles but there's actually b = 7 marbles, then she would be a-b = 10-7 = 3 marbles off.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For cases when b is larger than a, like a = 7 and b = 10, we have<BR>\n" );
document.write( "a-b = 7-10 = -3<BR>\n" );
document.write( "We can't have a negative distance. We want to be able to express this gap as some positive number or zero.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is where absolute value comes in.<BR>\n" );
document.write( "|a-b| ensures that the difference is never negative.<BR>\n" );
document.write( "The lowest it can go is 0. <BR>\n" );
document.write( "It represents the distance from a to b on the number line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To be within 15 marbles means that the distance |a-b| is 15 or smaller<BR>\n" );
document.write( "Put another way: the worst Ashley could guess is that she's 15 too high or 15 too low compared to the actual count.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This leads us to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28a-b%29+%3C=+15 ALIGN=MIDDLE  ALT=\"abs%28a-b%29+%3C=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That directly points to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15+%3C=+a-b+%3C=+15 ALIGN=MIDDLE  ALT=\"-15+%3C=+a-b+%3C=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > based on the rule that <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%29+%3C=+k ALIGN=MIDDLE  ALT=\"abs%28x%29+%3C=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-k+%3C=+x+%3C=+k ALIGN=MIDDLE  ALT=\"-k+%3C=+x+%3C=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > for any positive number k.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: Choice A  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15+%3C=+a-b+%3C=+15 ALIGN=MIDDLE  ALT=\"-15+%3C=+a-b+%3C=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );