Learn Before
Example: Solving the Inequality
To solve the linear inequality , the variable must be isolated. First, subtract from both sides to obtain . Next, divide both sides by to find the solution .
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Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
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Example: Solving and Graphing
Example: Solving and Graphing
Example: Solving and Graphing
Solving the Linear Inequality
A logistics coordinator is using the inequality to determine the maximum number of additional crates, , that can be added to a shipment without exceeding a weight limit. To isolate in the final step of the solution, the coordinator must divide both sides by -2. Which rule must be recalled when performing this operation?
A production manager is solving a multi-step linear inequality to determine the minimum number of units a factory must produce to stay within a specific budget. Arrange the following steps in the standard order typically used to solve a multi-step linear inequality for a variable, such as .
A procurement officer is solving the inequality to stay within a quarterly budget for office supplies, where represents the number of units ordered. After simplifying the inequality to , the officer must divide both sides by to solve for . True or False: In this final step, the inequality sign must be reversed to to maintain the correct solution.
Simplifying Multi-Step Inequalities
A business operations manager is solving a multi-step linear inequality to determine the maximum number of safety inspections that can be performed within a fixed quarterly budget. Match each algebraic property or rule to the correct description of its role in the solution process.
An inventory analyst is solving a multi-step linear inequality to ensure warehouse storage costs remain under a specified budget. In the final step of the calculation, they must divide both sides of the inequality by a negative number to isolate the variable. To maintain a true statement, the analyst must ________ the direction of the inequality sign.
Budget Calculation Review
Example: Solving and Graphing
Example: Solving and Graphing
Example: Solving the Inequality
Learn After
As a logistics coordinator, you use the expression to determine the total shipping cost in dollars, where is the number of expedited packages. If the total cost exceeds 23 dollars, the system flags the order for review, modeled by the inequality . Recalling the standard algebraic sequence to isolate a variable, what is the correct solution for ?
You are a facility manager at a corporate campus calculating the threshold for extra maintenance hours () during a major renovation project. Your budget requires that the total labor cost, represented by the expression , must exceed 23 dollars per unit of work to trigger a secondary funding source, modeled by the inequality . To determine the point at which this funding is activated, you must solve for . 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 to determine when to trigger a surcharge alert, where 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 to determine the minimum number of units () required to qualify for a corporate bulk discount. After performing the necessary algebraic steps to isolate , 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, , required to meet a daily outreach target. The clinic's scheduling formula is represented by the inequality . 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 .
Calculating Extra Staffing Hours