Suppose that \(|a - b| + |b - c| + |c - a| = 20\) What is the maximum possible value of \(|a-b|\)?

l a - b l will be maximized when a is large as possible and b is as small as possible

So....suppose that a > c > b

Then we have that

(a - b) +( c - b) + ( a - c) = 20

2a - 2b = 20 divide through by 2

a - b = 10

So

l a - b l = 10