In a logistics optimization task, you are evaluating a performance ratio modeled by the expression $\frac{x-2}{x+4}$. To find the range of values where this ratio is non-positive ($\frac{x-2}{x+4} \leq 0$), you must follow a standard solution procedure. Arrange the following steps in the correct chronological order as described in the course material.

As an inventory analyst, you are evaluating a surplus-to-demand ratio modeled by the expression $\frac{x-2}{x+4}$. To ensure the surplus ratio remains at or below the acceptable threshold of zero, you are tasked with solving the rational inequality $\frac{x-2}{x+4} \leq 0$. Based on the standard procedure for finding the partition numbers and testing the intervals, which of the following is the correct solution set expressed in interval notation?

In a corporate performance evaluation, you are using the rational inequality $\frac{x-2}{x+4} \leq 0$ to identify a range of acceptable efficiency scores ($x$). To correctly solve this, you must recall the specific roles of the values derived from the expression. Match each term below with its correct definition or property based on the standard solution procedure.

In a corporate resource allocation model using the rational inequality $\frac{x-2}{x+4} \leq 0$, the value $x = -4$ is included in the final solution set because the inequality uses the 'less than or equal to' symbol.

Partition Numbers in Budget Variance Models

As a risk assessment analyst, you are solving the rational inequality $\frac{x-2}{x+4} \leq 0$ to find acceptable project risk levels ($x$). You recall from the standard procedure that the partition number $x = -4$ must be excluded from the final solution interval because it makes the denominator zero and therefore makes the function ____.