In which context is isolating a variable considered "sufficient"?

Isolating a variable is considered "sufficient" in the context when it can be evaluated within a set of known values because this scenario allows for clear calculations and solutions. By having the variable isolated, one can substitute known values into the equation or expression safely, facilitating the evaluation and leading to a definitive result.

When a variable is isolated, it means that the equation has been manipulated in such a way that the variable stands alone on one side. This clear definition enables easy evaluation—not only does it highlight the relationship between the variable and known quantities, but it also ensures that one’s calculations will be accurate and effective in deriving the required outcome. In many mathematical and statistical applications, knowing exact values for other variables and having them related to the isolated variable can lead to better insights and understanding.

The other situations described do not align with the idea of sufficiency. For example, solving for a variable directly may be a goal, but it doesn't necessarily imply sufficiency without known values or without the context provided in the other answers. Similarly, the presence of the variable in an equation doesn't mean it can be easily evaluated without isolation. When a variable is absent, it precludes any possibility of evaluating its value at all.