<p>Hi Guys. I am having trouble with the following question.Help appreciated.
If 6<x-3<7 and x<o,what is one possible absolute value of x? Please note that x-3 and x are absolute values.I couldnot figure out the sign of absolute value on the key.Thanks! This question is from previous years 2010-2011 SAT tests.</p>
<p>-4< x <-3, so the absolute value of x, which value you would enter into the grid in, would be anything between 3 and 4. 3.5 is a lovely potential answer.</p>
<p>Thanks for the “lovely potential answer”.</p>
<p>It says “x<0,” so I think you must choose a different potential answer.</p>
<p>For a more intuitive way to solve this problem:
Whenever you have a absolute value sign being greater than or less than a number that means that the problem has two solutions. In this case, its easier to take the second part of the equation first. So 6<abs(x-3). That means that the soln’s could be 6<x-3 or -6<x-3. So the potential solutions are 9<x and -3<x. However, the other restriction is that x<7. Therefore the first soln doesnt work. Thus we go to the next solution. If we plug in -4 into the equation we get 6<abs(-7)<7. That doesn’t work. Therefore, we just use a fraction, ie. -3.5</p>