Final answer:
A vector should be expressed as negative when it points in the opposite direction to the one designated as positive in your coordinate system. For example, if rightward is positive, then a vector pointing leftward is negative. The choice of positive and negative directions is arbitrary but must be consistent in your analysis.
Step-by-step explanation:
You should express a vector along the x-axis as a negative vector when it points in the direction opposite to the one defined as positive in your coordinate system. In many contexts, the right direction is considered positive, and thus a vector pointing to the left would be negative. However, it's essential to note that the choice of positive and negative is arbitrary and should be consistent within a given problem. For example, if a person is running to the left and you choose to define left as positive for your analysis, then movements to the right would be expressed by negative vectors.
When dealing with vector components, if the x-component is negative, this indicates that the vector is directed to the left, away from the positive x-direction defined by the unit vector i. This is particularly important when you're adding or subtracting vectors, as you will adjust the magnitudes accordingly and include the direction as part of the final answer.