Re: How many values can the integer p=|x+3|-|x-3| assume?

How many values can the integer p=|x+3|-|x-3| assume?

Checkpoints at -3, 3

x<-3, -3<x<3, x>3

x<-3:
p=|x+3|-|x-3|
p=-(x+3) - -(x-3)
p= -x-3 - (-x+3)
p= -x-3 + x -3
p= -6

-3<x<3
p=|x+3|-|x-3|
p= (x+3) - -(x-3)
p= x+3 + x -3
p= 2x

x>3
p=|x+3|-|x-3|
p=(x+3)-(x-3)
p= 6

So the range of p is from -6 to 6. There are a total of 13 integers between -6 and 6

(C) 13