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.