Learn Before
Solving
Solve the linear inequality by applying the Multiplication Property of Inequality.
Step 1 — Multiply both sides by : Because the variable is divided by a negative number, multiplying both sides by requires reversing the inequality sign:
Step 2 — Simplify: Evaluate the product on the right side:
Step 3 — Write the solution in interval notation: The solution includes and all real numbers less than , which is written as .
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Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
Algebra
Related
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
In a logistics calculation, a coordinator uses the inequality to define a constraint for . What is the correct solution for ?
An inventory manager calculates a stock requirement using the inequality . To solve for , the manager multiplies both sides by and determines that the final solution is .
A warehouse manager is calculating a safety threshold for load distribution on a shelving unit. The constraint is represented by the inequality . Arrange the following steps in the correct order to solve for the maximum allowable value of .
A warehouse supervisor is monitoring a load limit for a conveyor belt, represented by the inequality . Based on the rules for solving inequalities, match each part of the solution process with its correct value or representation.
Logic Implementation for Safety Constraints