Explain why solving an equation containing one absolute value expression does not apply to the expression | x - 5 | = -3?

One useful and naturally intuitive definition is that the absolute value of an number is it's distance from 0 on the number line. If we use this definition then we require that the absolute value of a real valued quantity be greater than or equal to zero. We also know that both sides of any equation must have the same sign to have a solution- therefore this equation is a contradiction.