In a manufacturing environment, a technician is calibrating a sensor. The sensor is considered active only when the input value $x$ satisfies both ${}2(3x+1) \leq 20$ and ${}4(x-1) < 2$. Based on the mathematical solution for this compound inequality, which interval notation correctly represents the values of $x$ for which the sensor is active?

In a manufacturing facility, a quality control engineer is establishing the allowable pressure adjustment range $x$ for a specialized valve. The adjustment must simultaneously satisfy two safety protocols: ${}2(3x+1) \leq 20$ and ${}4(x-1) < 2$. Arrange the following steps in the correct order to solve this compound inequality and identify the final overlapping safety interval in interval notation.

In a manufacturing facility, a technician is calibrating a sensor that must operate within the limits defined by the compound inequality ${}2(3x+1) \leq 20$ and ${}4(x-1) < 2$. Match each part of the solution process with its corresponding mathematical result.

True or False: When solving the compound inequality ${}2(3x+1) \leq 20$ and ${}4(x-1) < 2$, the solution to the first inequality is $x \leq 3$ and the solution to the second inequality is $x < \frac{3}{2}$.

Quality Control Safety Intervals