<PRE><B>Question 1206363</B>
&lt;br&gt;
Donna and Kayleigh both go to the same high school. Donna lives 21 miles from the school. Kayleigh lives 6 miles from Donna.&lt;br&gt;
Kayleigh lives somewhere on a circle with radius 6 miles with center at Donna&#39;s house.  So the distance from Kayleigh&#39;s house to the school can be anything from some minimum to some maximum.  It should be obvious that the minimum and maximum distances of Kayleigh&#39;s house from the school are if the school and the two girls&#39; houses lie in a straight line.&lt;br&gt;
Part A. Write an absolute value equation to represent the location of Kayleigh’s house in relation to the high school.&lt;br&gt;
That is poorly written.  What is in fact needed (I think!) is an absolute value INEQUALITY that can be solved to find the range of possible distances from Kayleigh&#39;s house to the school.&lt;br&gt;
That inequality says that the difference between the distance x of Kayleigh&#39;s house to the school and the distance of Donna&#39;s house from the school (21 miles) is at most 6 miles:&lt;br&gt;
{{{abs(x-21)&lt;=6}}}&lt;br&gt;
Part B. How far could Kayleigh live from her school?&lt;br&gt;
Informally, the distance from Kayleigh&#39;s house to the school is at least 21-6 = 15 miles and at most 21+6 = 27 miles.&lt;br&gt;
Formally....&lt;br&gt;
{{{abs(x-21)&lt;=6}}}
{{{-6&lt;=x-21&lt;=6}}}
{{{-6+21&lt;=x&lt;=6+21}}}
{{{15&lt;=x&lt;=27}}}&lt;br&gt;
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