How many solutions should you have when solving absolute value equation when possible?

When solving an absolute value equation, you can typically have two solutions, one for each case where the expression inside the absolute value can be either positive or negative. For example, the equation |x| = a has the solutions x = a and x = -a, assuming a is non-negative. However, if the equation results in a negative value inside the absolute value, there will be no solutions, as absolute values cannot be negative.