A project coordinator is solving the inequality $\frac{u}{-4} \geq -16$ to determine the maximum budget allocation for a department. To isolate the variable $u$, the coordinator must multiply both sides of the inequality by ${}-4$. According to the properties of inequalities, how must the inequality symbol be handled during this step?

A logistics coordinator is solving the inequality $-7r \leq -70$ to determine the minimum number of shipment reductions, $r$, required to meet a new efficiency target. True or False: To isolate $r$, the coordinator must divide both sides by $-7$ and reverse the inequality symbol from $\leq$ to $\geq$.

A facilities manager is calculating the minimum number of safety inspections, $r$, required for a warehouse expansion using the inequality $-7r \leq -70$. Arrange the steps in the correct order to solve this inequality for $r$.

A facility manager is evaluating two different operational constraints: one for the number of shipments, $r$, modeled by ${}-7r \leq -70$, and another for the total units, $u$, modeled by $\frac{u}{-4} \geq -16$. Match each inequality with its corresponding solution and its correct interval notation.

Maintaining Inequality Direction in Maintenance Schedules

During a corporate budget review, a financial planner is solving the inequality $\frac{u}{-4} \geq -16$ to determine acceptable departmental spending limits. To isolate the variable $u$, they multiply both sides by $-4$. According to the properties of inequalities, whenever both sides of an inequality are multiplied or divided by a negative number, the planner must ____ the direction of the inequality symbol.