A logistics manager determines that a specific operational factor $x$ must satisfy two safety constraints simultaneously: ${}4x - 7 < 9$ and ${}5x + 8 \geq 3$. Based on the solution to these inequalities provided in the course material, which interval notation correctly represents the valid range for $x$?

During a workshop on supply chain tolerances, you review the compound inequality ${}4x - 7 < 9$ and ${}5x + 8 \geq 3$. In the final overlapping solution, the boundary -1 is included, while the boundary 4 is not.

A quality control technician is calibrating a sensor where the allowed variance $x$ must satisfy two safety constraints: ${}4x - 7 < 9$ and ${}5x + 8 \geq 3$. Arrange the following steps in the correct chronological order to determine the final interval notation for the allowed variance.

An inventory specialist is calculating the optimal storage volume ($x$) for a new product line. To meet safety standards, the volume must satisfy two regulations simultaneously: ${}4x - 7 < 9$ and ${}5x + 8 \geq 3$. Match each part of the regulatory calculation process to its corresponding mathematical result.

A warehouse logistics coordinator is checking the weight variance ($x$) allowed for a specific shipment. To meet safety standards, the variance must satisfy two automated rules: Rule 1 is ${}4x - 7 < 9$ and Rule 2 is ${}5x + 8 \geq 3$. According to the solution provided in the course material, the final overlapping solution set expressed in interval notation is ____.