Final answer:
In real world applications, a negative result for an absolute value equation doesn't make sense for scalar quantities where a negative magnitude is impossible, such as distance or time events before their initiation. Displacement as a vector can have negative values indicating direction, but distance as a scalar cannot. Checking for reasonable results ensures practical interpretation of outcomes.
Step-by-step explanation:
For certain real world quantities, a negative answer for an absolute value equation would not make sense. In physics and other sciences, negative results from equations can indicate a direction opposite to a chosen positive direction in a coordinate system. However, certain physical quantities, such as distance, are scalar quantities that are magnitude-only metrics without an inherent direction. In these contexts, absolute values are always non-negative. When solving equations involving such quantities, a negative solution can be considered physically impossible or nonsensical and should thus be discarded.
An example would be the calculation of a displacement. If the displacement of an object is described as -100 m, it means that the displacement is 100 m in the direction opposite to the chosen positive direction. It makes sense in this context because displacement is a vector quantity; it has both magnitude and direction. However, distance, another scalar quantity, cannot be negative since it represents the magnitude of the displacement without considering its direction.
Moreover, in situations like determining time values from quadratic equations, a negative time result can occur. This negative solution does not align with our experience as time before the initiation of an event does not physically make sense in context. For example, the negative root in a time variable quadratic equation relating to the motion of an object would correspond to a time before the object was released or before the event occurred, which is not meaningful in real-world scenarios.
It is crucial in scientific problem-solving to check if the answer is reasonable. This involves ensuring the answer's magnitude is sensible and that signs and units are correct. In homework and tests, numbers might come pre-loaded with defined exact values, but in real world applications, estimations and approximations are often necessary and must make practical sense. Since real-world quantities can be vectors or scalars, understanding the properties of the quantity in question is essential when interpreting the outcomes of equations and whether a negative absolute value solution is plausible.