What is the minimum value of |x-4| + |x+7| + |x-5| ?

A cannot be the answer as all the three terms are in modulus and hence the answer will be non negative.
|x-4| >= 0 --> Minimum occurs at x = 4
|x+7| >= 0 --> Minimum occurs at x = -7
|x-5| >= 0 --> Minimum occurs at x = 5
x = -7 --> Result = 11 + 0 + 12 = 23. Also any negative value will push the combined value of |x-4| + |x-5| to a value > 9.
x = 4 --> Result = 0 + 11 + 1 =12
x = 5 --> Result = 1 + 12 + 0 = 13
x = 7 --> Result = 3 + 14 + 2 = 19
So minimum value of the expression occurs at x = 4 and the resultant value = 12
Answer: E