document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206363>Question 1206363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Donna and Kayleigh both go to the same high school. Donna lives 21 miles from the school.Kayleigh lives 6 miles from Donna.<BR>\n" );
document.write( "Part A. Write an absolute value equation to represent the location of Kayleigh’s house in relation to the high school.<BR>\n" );
document.write( "Part B. How far could Kayleigh live from her school?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843776 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=843776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> donna lives 21 miles from the school.<BR>\n" );
document.write( "kayleigh lives 6 miles from donna.<BR>\n" );
document.write( "the absolute value inequality that models this would be abs(x - 21) <= 6<BR>\n" );
document.write( "this says that the maximum distance from the school to kayleigh's house will be 21 + 6 = 27 miles and the minimum distance from the school to kayleigh's house will be 21 - 6 = 15 miles.\r<BR>\n" );
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document.write( "the absolute value inequality is solved by breaking it up into two separate parts.<BR>\n" );
document.write( "the first part assumes x - 21 is positive and the second part assumes x - 21 is negative.\r<BR>\n" );
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document.write( "first part is (x-21) <= 6.<BR>\n" );
document.write( "add 21 to both sides of that inequality to get x <= 27\r<BR>\n" );
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document.write( "second part is -(x-21) <= 6<BR>\n" );
document.write( "multiply both sides of that by -1 to get (x-21) >= -6.<BR>\n" );
document.write( "that's because multiplying both sides of an inequality by a negative number reverses the inequality.<BR>\n" );
document.write( "solve for x to get x >= 15.\r<BR>\n" );
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document.write( "the smallest distance from kayleigh to the school is 15.<BR>\n" );
document.write( "the largest distance from kayleigh to the school is 27.\r<BR>\n" );
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document.write( "here's a reference on absolute value equalities and inequalities.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/02%3A_Graphing_Functions_and_Inequalities/206%3A_Solving_Absolute_Value_Equations_and_Inequalities\" target = \"_blank\">https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/02%3A_Graphing_Functions_and_Inequalities/206%3A_Solving_Absolute_Value_Equations_and_Inequalities</a>\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo<BR>\n" );
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