Consider 3 casesrahul.s wrote:Is |x| + |x - 1| = 1?
1) x => 0
2) x <= 1
a) if x is greater than one
|x| + |x - 1| is not equal to one (it is greater)
b) if x is less than zero then
|x| + |x - 1| is not equal to one (it is greater)
c) Now if x is in between 1 and 0 (both included)
|x| + |x - 1| is equal to 1
since 1 and 2 both together gives condition 'c'
both statements together are enough to validate the claim
[ Get to the boundary conditions of the sign change (of the absolute function) and evaluate each segment in the number line ]
