In quality control testing, a manufactured component must satisfy two stress-test conditions simultaneously to pass inspection: ${}3(2x+5) \leq 18$ and ${}2(x-7) < -6$. You have already simplified these conditions down to $x \leq \frac{1}{2}$ and $x < 4$. Recalling the mathematical rule for compound inequalities joined by the word "and", what is the final acceptable range of values for $x$ expressed in interval notation?

A quality control supervisor is reviewing the safety specifications for a high-pressure chemical valve. The valve's operating pressure $x$ (in kilopascals) must satisfy two distinct safety conditions simultaneously: ${}3(2x+5) \leq 18$ and ${}2(x-7) < -6$. Match each part of the mathematical evaluation with its corresponding result from the safety analysis.

A warehouse safety inspector must determine the safe load limit $x$ (in tons) for a racking system. The limit must satisfy two conditions simultaneously: ${}3(2x+5) \leq 18$ and ${}2(x-7) < -6$. Arrange the following steps in the correct order to find the final safe range for $x$.

In a logistics safety audit, a technician evaluates a weight limit $x$ that must satisfy the compound inequality ${}3(2x+5) \leq 18$ and ${}2(x-7) < -6$. After simplifying these conditions to $x \leq \frac{1}{2}$ and $x < 4$, the technician concludes that the final combined safety range, expressed in interval notation, is $(-\infty, \frac{1}{2}]$. Is the technician's conclusion correct?

Pneumatic Lift Safety Tolerance

In a heavy machinery safety audit, a technician determines that a stress-load factor $x$ must satisfy the compound inequality ${}3(2x+5) \leq 18$ and ${}2(x-7) < -6$ simultaneously. After solving and finding the overlap of these two conditions, the final safe operating range expressed in interval notation is ____.