Consider that a and b are positive number such that \(a < b\).

Recall that the absolute difference of two number is a positive number.

So, the expression \(| x – b |\) is always a positive number for all values of x.

But -a is a negative number since a is a positive number.

Since the left-hand side of the equation \(|x − b| = -a\) is a positive number and right-hand side of the equation \(|x − b| = -a\) is a negative number hence the equation \(|x − b| = -a\) has no solution.