Learn Before
Example: Translating and Solving 'Twenty-seven less than is at least 48'
To translate and solve the sentence "Twenty-seven less than is at least 48," apply a step-by-step translation process:
- Translate the left side: The phrase "Twenty-seven less than " indicates subtraction from , giving the expression .
- Translate the inequality: The phrase "is at least" signifies a minimum limit, which corresponds to the "greater than or equal to" symbol, .
Combining these elements generates the inequality .
To solve the inequality, isolate by applying the Addition Property of Inequality—add to both sides:
To represent the solution set visually on a number line, a left bracket is placed at to indicate it is included, and shading continues to the right. In interval notation, this is expressed as [75, infty).
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Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
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Related
Identifying Inequality Properties in Logistics
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'
If , which property guarantees that ?
If , then adding a negative number to both sides gives .
Given , put the steps in order to show .
Adding the same number to both sides of an inequality without changing its direction is called the ______ Property of Inequality.
If , then for any number .
Match each term to its meaning for the Addition Property of Inequality.
Read the case below, then answer the questions that follow.
If , and the same number is added to both sides, which statement is true?
If , then for any number . Name this property and explain why the inequality symbol stays the same.
Learn After
A project manager is calculating the minimum weight requirement for a shipping platform and determines that 'twenty-seven less than the total weight () must be at least 48 tons.' Which of the following inequalities correctly translates this requirement?
A logistics coordinator needs to calculate a minimum warehouse capacity requirement. The protocol states: 'Twenty-seven less than the current capacity () must be at least 48 units.' Arrange the following steps in the correct order to translate this statement into an inequality and solve for the required capacity .
A corporate performance report includes the following requirement: "Twenty-seven less than the production goal () is at least 48." Match each component of this requirement with its correct mathematical translation or notation.
Translating Inventory Requirements
A facility manager is reviewing a safety guideline: 'Twenty-seven less than the maximum occupancy () must be at least 48.' The phrase 'Twenty-seven less than ' is correctly translated into the mathematical expression .
A regional sales coordinator is tracking quarterly customer acquisition targets. The corporate performance policy requires that 'twenty-seven less than the target number of new sign-ups () must be at least 48.' When translating this policy into a mathematical inequality, the phrase 'twenty-seven less than ' represents a subtraction from , which is written as the algebraic expression ____.
Translating and Interpreting Threshold Requirements