Solving the Linear Inequality $2a < 5a + 12$

As a logistics coordinator, you use the expression ${}4x + 3$ to determine the total shipping cost in dollars, where $x$ is the number of expedited packages. If the total cost exceeds 23 dollars, the system flags the order for review, modeled by the inequality ${}4x + 3 > 23$. Recalling the standard algebraic sequence to isolate a variable, what is the correct solution for $x$?

You are a facility manager at a corporate campus calculating the threshold for extra maintenance hours ($x$) during a major renovation project. Your budget requires that the total labor cost, represented by the expression ${}4x + 3$, must exceed 23 dollars per unit of work to trigger a secondary funding source, modeled by the inequality ${}4x + 3 > 23$. To determine the point at which this funding is activated, you must solve for $x$. Arrange the following steps in the correct algebraic sequence to isolate the variable.

A telecommunications billing analyst is auditing an automated system that flags accounts for excessive data usage. The system uses the inequality ${}4x + 3 > 23$ to determine when to trigger a surcharge alert, where $x$ represents the number of additional gigabytes used. To verify the audit logic, match each component of the solution process with its correct algebraic description or result.

Operational Expense Threshold

A procurement analyst uses the inequality ${}4x + 3 > 23$ to determine the minimum number of units ($x$) required to qualify for a corporate bulk discount. After performing the necessary algebraic steps to isolate $x$, the analyst finds that the number of units must be greater than ____.

An administrative assistant at a local healthcare clinic is calculating the minimum number of additional patient scheduling slots, $x$, required to meet a daily outreach target. The clinic's scheduling formula is represented by the inequality ${}4x + 3 > 23$. When solving this inequality to verify the system's threshold, the correct first step to isolate the variable is to subtract 3 from both sides, which simplifies the inequality to ${}4x > 20$.

Calculating Extra Staffing Hours