True or False - absolute value inequality

True or False: The absolute value inequality |x-a|
Help?

No! Let b = 0. Then |x - a| < 0 which is impossible for any x.

lets see
x-a can be positive that would be true if x-a is less than b and x is not greater than a+b but not guaranteed
or x-a is negative that would be true if x is greater than b-a , but that is not guaranteed.

so it would appear that a+b < x or
a+b < x and
a-b < x

adding 2a < 2x
a
-

The absolute value of |x-a| will always equal to the positive values of those numbers (which is constant) however there is a variable which is b. So the answer is True because you can arrive to at least one solution because of the variable.