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Addition Property of Equality
The Addition Property of Equality states that if the same quantity is added to both sides of an equation, the two sides remain equal. Mathematically, for any numbers , , and :
If , then
This property is a fundamental tool used to solve equations where a number is subtracted from the variable. To isolate the variable and "undo" the subtraction, the same number is added to both sides. For example, when solving an equation like , adding to both sides isolates while maintaining the equality.
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When an office manager uses a formula to calculate a missing expense, the primary mathematical goal is to ____ the unknown variable by itself on one side of the equation.
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In a workplace scenario, such as calculating the number of hours an employee worked based on their total earnings, the ultimate mathematical purpose of solving the resulting equation is to find a specific value for the variable that creates a true statement.
A project manager is solving an algebraic equation to determine the number of additional staff members needed for a new contract. Arrange the following conceptual stages of 'solving an equation' in the correct logical order, according to the standard mathematical definition.
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A laboratory technician is solving an equation to determine the exact amount of a catalyst needed for a chemical reaction. According to the definition of solving an equation, what is the defining characteristic of the specific value (the solution) the technician is searching for?
A project coordinator is reviewing the process of finding unknown values in a budget report. Match each aspect of the mathematical process of 'solving an equation' with its correct description according to the standard definition.
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Extended Addition Property of Equality
A logistics supervisor is balancing two shipping scales that currently show the same weight (a = b). If the supervisor places a 5-pound calibration weight (c) on both scales, which equation represents the Addition Property of Equality?
In a corporate budgeting spreadsheet, if the projected revenue for Department A is equal to the projected revenue for Department B, adding the same year-end bonus amount to both totals will ensure the revenues remain equal. This principle is defined as the ____ Property of Equality.
In a warehouse inventory system, if Bin A and Bin B contain the same number of items, adding 10 additional items to both bins will ensure they still contain an equal number of items. This principle is known as the Addition Property of Equality.
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A business administrator is adjusting financial records to ensure that balance is maintained across identical accounts. Match the following terms related to the Addition Property of Equality with their correct descriptions or examples.
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A project manager needs to adjust two departmental budgets that are currently identical. Arrange the steps in the correct order to demonstrate the application of the Addition Property of Equality when adding a uniform 'overhead allowance' to both budgets.
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A warehouse supervisor is balancing inventory counts between two identical storage units that currently hold the same number of items. If the supervisor adds 25 additional items to the first unit, what action does the Addition Property of Equality require to ensure the units still contain an equal number of items?
A retail analyst is using the equation x - 20 = 80 to determine the original stock level (x) of a product after 20 units were sold. To isolate the variable x by adding 20 to both sides of the equation, which mathematical property must the analyst recall?