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.

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.