Learning Objectives for Graphing Systems of Linear Inequalities

A facility manager uses the linear inequality $y > 2x + 3$ to determine if the available power load $y$ is sufficient for a specific number of machines $x$. If the manager tests a scenario with the ordered pair $(3, \frac{1}{2})$, which of the following statements correctly identifies whether this pair is a solution?

A solar energy technician uses the linear inequality $y > 2x + 3$ to check if the current energy output $y$ (in kilowatts) exceeds the minimum requirement for $x$ active solar panels. True or False: When substituting the test coordinates $(3, \frac{1}{2})$ into this inequality, the resulting mathematical statement is true.

A warehouse manager uses the linear inequality $y > 2x + 3$ to determine if the available storage space $y$ (in units) is sufficient for the number of incoming shipments $x$. To check if the specific scenario represented by the data point $(3, \frac{1}{2})$ complies with safety protocols, arrange the following procedural steps in the correct logical order.

A production supervisor uses the linear inequality $y > 2x + 3$ to check if the available cooling time $y$ (in hours) is sufficient for $x$ manufacturing cycles. When evaluating whether the specific case (3, rac{1}{2}) satisfies this standard, the supervisor substitutes the coordinates into the inequality. After simplifying the expression on the right-hand side, the resulting mathematical statement is $\frac{1}{2} >$ ____.

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