In a manufacturing quality control process, the variable $v$ represents the variance of a part's width from the target specification. Match each absolute value equation to the correct description of its solution set.

In a warehouse inventory audit, a manager uses the variable $v$ to represent the difference between the actual stock and the recorded stock. Which of the following absolute value equations would indicate a logical error in the reporting system because it has no possible solution?

In a manufacturing quality control process, a technician uses the equation $|y| = -4$ to represent the deviation of a part's thickness from the target. In this situation, the technician should correctly conclude that the equation has exactly two solutions: $y = 4$ and $y = -4$.

Shipping Variance Evaluation

A precision machinist is analyzing the error margins for three different parts using absolute value equations. The variable represents the deviation from the target measurement. Arrange the following equations in order based on the number of possible solutions they have, starting with the equation that has the fewest solutions and ending with the equation that has the most solutions.

A logistics coordinator is tracking delivery time variances. They encounter the equation $|v| = -4$ while reviewing the data. Because an absolute value represents a distance and cannot be negative, the coordinator recalls that this equation has ____ valid solutions.