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Training Manual: Rules for the Multiplication Property of Inequality
You are drafting a mathematical reference guide for a group of operations managers who use inequalities to set production thresholds. In your guide, state the specific rules for the Multiplication Property of Inequality. Specifically, describe what happens to the direction of the inequality symbol when both sides are multiplied by a positive number versus a negative number. Additionally, identify the key difference between how this property affects an inequality compared to how the Multiplication Property of Equality affects an equation.
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Elementary Algebra @ OpenStax
Algebra
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A project manager is using an inequality to ensure that project costs do not exceed the allocated budget. According to the Multiplication Property of Inequality, which operation would require the manager to flip the inequality symbol?
When a warehouse supervisor multiplies both sides of an inventory inequality by a positive number, the Multiplication Property of Inequality states that the direction of the inequality symbol must be reversed.
A project manager is adjusting budget inequalities to account for cost changes. Match each mathematical operation with the correct rule for the inequality symbol according to the Multiplication Property of Inequality.
According to the Multiplication Property of Inequality, if a logistics manager multiplies both sides of an inequality by a negative number while calculating shipping constraints, the direction of the inequality symbol must be ________.
Applying the Multiplication Property of Inequality in Auditing
A budget analyst is adjusting financial constraints to account for a negative growth factor. According to the Multiplication Property of Inequality, arrange the following steps in the correct order to apply a negative multiplier to an existing inequality.
Revenue Forecasting and the Sign Reversal Rule
Training Manual: Rules for the Multiplication Property of Inequality
A warehouse manager is adjusting inventory minimums by a positive scaling factor. According to the Multiplication Property of Inequality, if the manager multiplies both sides of an inventory inequality by a positive number, what happens to the direction of the inequality symbol?
A logistics coordinator is analyzing a fuel consumption inequality for a delivery fleet. During the calculation, the coordinator needs to divide both sides of the inequality by -12 to isolate the variable. According to the Multiplication Property of Inequality, what must happen to the inequality symbol?
Solving
Example: Demonstrating the Multiplication and Division Properties of Inequality with a Positive Number
Example: Demonstrating the Multiplication and Division Properties of Inequality with a Negative Number
Example: Solving and Graphing
Example: Solving and Graphing
Example: Solving and Graphing