A quality control specialist is using the inequality $-8q < 32$ to determine the acceptable range of variance for a mechanical part. To isolate the variable $q$, the specialist divides both sides of the inequality by -8. According to the properties of inequalities, which of the following is the correct rule to apply to the inequality symbol in this step?

An operations manager at a logistics firm uses the inequality $\frac{k}{-12} \leq 15$ to determine the capacity $k$ of a storage system under specific budget constraints. Arrange the following steps in the correct order to solve for the capacity variable $k$.

In a corporate quality control department, an operations manager uses mathematical models to set production boundaries. Match each specific mathematical operation with the correct rule for adjusting the inequality symbol based on the properties of inequalities.

An inventory specialist is evaluating a cost constraint represented by the inequality $\frac{k}{-12} \leq 15$. To isolate the variable $k$, the specialist multiplies both sides of the inequality by $-12$. According to the properties of inequalities, because the specialist is multiplying by a negative number, the inequality symbol must be ______.

An operations manager is evaluating a production constraint modeled by the inequality $\frac{k}{-12} \leq 15$. When multiplying both sides of the inequality by $-12$ to isolate the variable $k$, the manager must keep the inequality symbol facing the same direction to maintain a true mathematical statement.

Applying Inequality Rules in Budget Constraints

Explaining Inequality Rules for Resource Planning Models