a home water system to prevent dry skin is between 20 and 26 pounds, inclusive. write an absolute value inequality that describes the needed weights

Question

I need help writing the inequality 

Answer 1

Here's how I think about absolute value; the absolute value is the distance away a specific thing is from some "center" value.  That should help explain why I'd approach this by finding the center of the range of values you've been given first and then finding the distance this ends up being from either end of the range.   The center is simply the average of the two ends: (20+26)/2, which should be easy to see is 23.  The range is clearly 6 (26-20, right?), so moving half of 6 in either direction from 23 (a +3 or -3 move) would get us to 20 and 26. 

 

So let's set up the possible values for w, which I'll use as the variable for the needed weights.

 

|w - center value| = 3 when it is inclusive, right?  So |w-23| = 3 should make sense so far.

 

Now what direction should the inequality symbol be?  Less than or greater than?  Well if you're not sure try using the center point as a possible number since it sounds like it should be a solution (since it has to be between 20 and 26).  You'd get |23-23| (?) 3.  Which inequality symbol would make the statement true?  Less than, of course.

 

So I'll leave you to write in the ≤ symbol.  Just remember that this sort of thing CAN be checked by working it from what you just wrote and making sure you remember how to solve an inequality for the two possible outcomes.