<p>if x is less than 0, </p>
<p>and 9 < absolute value of x minus 5 < 10, </p>
<p>what is one possible value of the absolute value of x minus 1</p>
<p>thanks!</p>
<p>say x= -4.5
| -4.5-5 |=9.5
This checks out in the inequality given.</p>
<p>-4.5-1= -5.5, your final answer</p>
<p>Here is a complete algebraic solution:</p>
<p>We break 9<|x-5|<10 into two pieces:</p>
<p>First piece:
|x-5|<10
-10<x-5<10
-5<x<15</p>
<p>Second piece:
|x-5|>9
x-5<-9 or x-5>9
x<-4 or x>14</p>
<p>Since we want x negative we take x<-4
This together with -5<x<15 yields -5<x<-4</p>
<p>So you can take any decimal strictly between -5 and -4.</p>
<p>Remark: On the SAT guessing and checking is the best strategy here. But I don’t see how this could be an SAT problem since you can’t grid in a negative number!</p>
<p>It depends if the OP is talking about |x|-5 or |x-5|. The same goes for |x-1| or |x|-1</p>
<p>Good point somewhere, the question is unclear. </p>
<p>I also just realized that I didn’t see the end of the question and just found the range of values for x (instead of abs(x-1) ).</p>
<p>If the OP wants to clarify the question I can give a more accurate solution.</p>
<p>My strategy for this is to just plug in numbers. :D</p>