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Addition Property of Inequality
The Addition Property of Inequality states that adding the same quantity to both sides of an inequality does not change the direction of the inequality. For any numbers , , and :
If , then
If , then
The same rule holds for and . This property is used to solve inequalities in which a number has been subtracted from the variable. To isolate the variable, the same number is added to both sides — just as with equations — and the inequality symbol stays pointed in the same direction. For example, to solve , adding to both sides gives , and the symbol remains unchanged.
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Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
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Addition Property of Inequality
Subtraction Property of Inequality
Multiplication Property of Inequality
Division Property of Inequality
Solution of an Inequality
Strategy for Solving Applications with Linear Inequalities
Solving a Rent Affordability Problem Using a Linear Inequality
Rounding Inequality Solutions to Whole Numbers in Applications
Solving a Budget-Constrained Purchase Problem Using a Linear Inequality
Linear Inequality in Two Variables
A logistics coordinator uses mathematical statements to ensure that shipping weights do not exceed a truck's capacity. When using a 'linear inequality' for this purpose, the variable in the expression must be raised to which power?
In a professional logistics context, a linear inequality (such as 'Weight <= 5000') typically results in only one specific numerical solution.
In a professional business environment, managers use specific mathematical symbols to define operational constraints and targets. Match each inequality symbol with the phrase that correctly describes its application in a workplace scenario.
Warehouse Capacity Planning
Visualizing Operational Thresholds
In a professional workplace, when a supervisor defines a budget limit or a safety threshold using a mathematical statement that connects two algebraic expressions with an inequality symbol and features a variable raised only to the first power, this statement is known as a(n) ________ ________.
Structural Requirements of Inequalities
A software developer is writing the logic for a budgeting tool that uses mathematical constraints to trigger alerts. Arrange the following structural components and characteristics in the correct order to describe the formal definition of a linear inequality.
A procurement officer uses a linear inequality to define the maximum price per unit they are willing to pay for a new contract. In this professional context, which of the following best defines the 'solutions' to that linear inequality?
A business analyst is organizing a training manual for a new budget tracking tool that uses mathematical constraints. Match each component of the tool's logic with its correct mathematical classification.
Example: Solving and Graphing One-Step Linear Inequalities
Solving Multi-Step Linear Inequalities
Collecting Variables on the Side with the Largest Coefficient When Solving Inequalities
Identity Inequality
Contradiction Inequality
Solving and Graphing Compound Inequalities with 'or'
Learning Objectives for Solving Linear Inequalities
Compound Inequality
Graphing the Solution Set of a Linear Inequality on a Number Line
Learn After
A logistics manager is comparing two shipping routes where Route A is shorter than Route B (A < B). If both routes are extended by the same 10-mile detour, which mathematical property ensures that Route A remains the shorter route (A + 10 < B + 10)?
If a project manager determines that the cost of 'Project Alpha' is less than 'Project Beta', the Addition Property of Inequality confirms that adding the same 2,000 dollars to both project budgets will result in 'Project Alpha' still costing less than 'Project Beta'.
Identifying Inequality Properties in Logistics
An operations manager observes that Assembly Line A produces fewer units per hour than Assembly Line B. If both lines receive a technical upgrade that increases production by exactly 50 units per hour for each line, the ______ Property of Inequality guarantees that Assembly Line A will still produce fewer units per hour than Assembly Line B.
In a corporate setting, budget and salary comparisons often rely on mathematical rules to ensure fairness. Match each term related to the Addition Property of Inequality with its correct description.
A logistics manager is comparing the fuel costs for two different delivery routes, Route A and Route B. Currently, the cost for Route A is less than the cost for Route B (Route A < Route B). If a flat fuel surcharge of $50 is added to both routes, arrange the following steps in the correct order to demonstrate the application of the Addition Property of Inequality.
Inventory Management and Inequality Properties
The Addition Property of Inequality in Payroll Adjustments
A department manager is reviewing quarterly expenses and notes that the costs for Department A () are less than the costs for Department B (). If a fixed corporate utility fee () is added to the expenses of both departments, which relationship is guaranteed to be true according to the Addition Property of Inequality?
A logistics supervisor is adjusting delivery timelines for two different shipping routes. If the supervisor applies a negative 'time-saving' adjustment to both sides of an inequality using the Addition Property of Inequality, the direction of the inequality symbol must be reversed.
Example: Demonstrating the Addition and Subtraction Properties of Inequality
Example: Solving and Graphing
Example: Solving and Graphing
Example: Solving and Graphing
Example: Translating and Solving 'Twenty-seven less than is at least 48'