A retail manager uses the inequality ${}3q \geq 7q - 23$ to determine the maximum number of items, $q$, that can be kept in a storage bin. Which of the following interval notations correctly represents the solution for $q$?

A project manager at a manufacturing plant uses the inequality ${}3q \geq 7q - 23$ to determine the production threshold for a specific component, where $q$ represents the number of batches produced. Arrange the following steps in the correct order to solve for $q$.

A fleet manager is solving the inequality ${}3q \geq 7q - 23$ to determine the maximum number of trucks, $q$, that can be assigned to a logistics route. After simplifying the inequality to the step $-4q \geq -23$, the manager must reverse the inequality symbol from $\geq$ to $\leq$ when dividing both sides by $-4$ to isolate the variable $q$.

An inventory manager is evaluating a storage capacity constraint modeled by the inequality ${}3q \geq 7q - 23$, where $q$ represents the number of supply crates. Match each stage of the solution process with the correct mathematical expression that results from that step.

A logistics planner is optimizing warehouse space based on the inequality ${}3q \geq 7q - 23$, where $q$ represents the number of pallets. After collecting the variable terms on the left side, the planner reaches the step $-4q \geq -23$. In the next step, the planner must divide both sides by $-4$. Because they are dividing by a negative number, the planner must remember to ____ the inequality sign to find the correct maximum number of pallets.