A facility manager is calculating the minimum number of maintenance personnel ($p$) required for a weekend shift using the inequality ${}8p + 3(p - 12) > 7p - 28$. Arrange the following steps in the correct order to solve the inequality and represent the solution.

An inventory supervisor is verifying the audit trail for a resource allocation calculation based on the inequality ${}8p + 3(p - 12) > 7p - 28$. To ensure the final report is accurate, match each description of the algebraic stage with the correct mathematical expression produced during that specific step.

A resource manager is calculating a minimum production quota ($p$) using the inequality ${}8p + 3(p - 12) > 7p - 28$. After simplifying the expression to the step ${}4p > 8$, the manager prepares to divide both sides by 4 to isolate $p$. True or False: In this specific step, the inequality symbol ($>$) must be reversed because a division operation is being performed.

Identifying Intermediate Steps in Linear Inequalities

An operations manager is using the inequality ${}8p + 3(p - 12) > 7p - 28$ to calculate $p$, the minimum number of production batches needed to meet a weekly quota. When graphing the final solution on a number line to visualize the valid batch quantities, the shading will stretch to the right, starting with a left parenthesis at the number ____.

Documenting Algorithmic Steps for Order Thresholds