<p>if 6< lx-3l <7 and x<0, what is one possible value of l x l</p>
<p>the things between the l l are absolute values</p>
<p>supposedly ur supposed to take out the three then it becomes</p>
<p>3< lxl < 4</p>
<p>and the asnwer is anything between 3 and 4</p>
<p>how does that work....</p>
<p>bump...anyone?</p>
<p>super confused..</p>
<p>Guess'n'check works the fastest:
try x=-3
|-3 - 3| = 6, not good</p>
<h1>|-3.5 - 3| = 6.5, bingo.</h1>
<p>Algebraically:
If x<0, then x-3<0, and by definition, |x-3| = -(x-3)
6< -x+3 <7, subtract 3
3< -x <4, multiply by -1, change the < signs
-3 > x > -4.
-3.5 will do.</p>
<p>the answers between 3 and 4</p>
<p>ur answers were 6.5 and -3.5</p>
<p>im more confused lol</p>
<p>6.5 is the value of |x-3|, -3.5 is the value of x, and 3.5 is the value of |x|.</p>
<p>Sorry stuntburn...
I wonder if your confusion is caused by the assumption that you can remove three from
6< lx-3l <7.</p>
<p>Just in case, here is the definition of | |:
........./ -a, if a<0
|a| = | 0, if a=0
.........\ a, if a>0</p>
<p>If you plug x=-3.5 into |x-3| you'll get
|x-3| = |-3.5 - 3| = |-6.5| = 6.5,
so for x=-3.5
6< |x-3| <7</p>
<p>Edit.
112358 beat me to the punch. :)</p>
<p>oooo lol</p>
<p>i think i get it now, its -3.5, but since the absolute value it becomes 3.5 </p>
<p>thanks alot guys</p>
<p>You are totally welcome, but I am afraid you either mistyped or missed something.</p>
<p>If you meant 6.5 instead of 3.5, than you got it right,
otherwise see this:</p>
<p>when x=-3.5
-3.5 does not become 3.5 in |x-3|:
|-3.5 - 3| =/= |3.5 - 3|.</p>
<p>|-3.5 - 3| = |-6.5|, and that becomes 6.5</p>
<p>oh ya, i understood that</p>
<p>but the question was what is the value of just lxl</p>
<p>and thats 3.5</p>
<p>oh right, I see, I misunderstood you.
You meant that all possible values of |x| are in the range from 3 to 4, and 3.5 works.
Gotcha.</p>