number line equation formation

by KK Thu Jun 26, 2008 2:09 am

on a number line if we are asked to form and equation for all values of x in absolute terms, starting -28 and going on to -15, what will be the equation and how is it formed. I was discussing it one of my friends and he said the answer would be

|x+21.5| < 6.5

how is this arrived at.

Waiting for response. Thanks

by **RonPurewal** Tue Jul 01, 2008 9:34 pm

so your friend gave you this answer, but didn't explain it? nice friends you've got. ha!

you can interpret absolute values CONCEPTUALLY in terms of DISTANCE: |x| is the distance between x and 0, and |x - y| is the distance between x and y.

for the range you've given, then, you should find the midpoint of the range, and then find out how far you have to go on each side of that midpoint. (this is so because the concept of "distance" is irrespective of whether the distance is to the left or to the right.)
the midpoint of the range is -21.5. each of the endpoints is 13/2 = 6.5 units away from this midpoint.
therefore,
(distance between x and -21.5) < 6.5
|x - (-21.5)| < 6.5
|x + 21.5| < 6.5

by KK Fri Jul 04, 2008 7:43 pm

Thanks

Your replies to all my posts really help. I was so lost earlier in inequalities.

by **rfernandez** Fri Jul 18, 2008 3:58 am

We're glad it's helpful!