Solve the following modulus equation: |x-1| = |x| +1

The modulus of a number x is a value equal to -x if x
< 0 and equal to x if x >= 0.

We have to
solve |x-1| = |x| +1

|x-1| = |x|
+1

If x - 1 > 0 => x > 1 or x >
0

=> x - 1 = x +
1,

=> -1 = 1, not
possible

If x - 1 =< 0 , x can be greater than or
equal to 0 or less than 0

=> 1 - x = x + 1 =>
x = 0

1 - x = -x + 1 => 1 = 1, always true. The
given equation is true for all values of
x<0

The required solution of the
equation is [-inf. , 0]