Learn Before
Example: Solving and Graphing
The linear inequality is solved using the Multiplication Property of Inequality. First, isolate the variable by multiplying both sides by the reciprocal of the coefficient, which is . Because is a positive number, the inequality sign is unchanged, returning the true statement . To make graphing more intuitive, this can be rewritten with the variable on the left as . The solution is then graphed on a number line with a left parenthesis at and shaded to the right. In interval notation, this represents the interval .
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Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate 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
Learn After
A supply chain analyst is determining the acceptable tolerance range for shipping delays, represented by , using the inequality . To solve for , the analyst multiplies both sides by the reciprocal, . Recalling the properties of inequalities, why does the direction of the inequality symbol remain unchanged (resulting in ) during this calculation?
An operations manager at a distribution center uses the inequality to determine the safe load adjustment (in tons) for a storage rack. Match each term of the solution process with its correct mathematical value or notation based on the steps for solving and graphing the result.
A facility manager is using the inequality to determine the minimum safety tolerance for a ventilation system. Arrange the following steps in the correct chronological order to solve the inequality and represent the solution graphically and in interval notation, according to the standard procedure.
A logistics coordinator determines that a safety threshold must satisfy the inequality . True or False: To correctly graph the solution set on a number line, a left parenthesis should be placed at and the line should be shaded to the right.
A logistics manager determines that a safety threshold must satisfy the inequality . To solve for , the manager multiplies both sides by , resulting in the boundary value for the solution set. When representing this solution in interval notation as documented in the procedure, the interval is written as (____, ).