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Absolute Value Inequality
An absolute value inequality is an inequality that contains an absolute value expression. When solving an absolute value inequality, the standard principles and procedures for solving basic inequalities still apply, but it is necessary to additionally consider how the properties of the absolute value impact the mathematical work.
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Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
Algebra
Related
Non-negative Property of Absolute Value
Simplifying Absolute Value Expressions
Evaluating , , and for Given Values
Defining Magnitude in Technical Reports
Auditing and Financial Deviations
Example of Absolute Value Evaluation
Example: Solving Basic Absolute Value Equations
Example: Solving
Example: Solving
Try It: Solving and
Example: Solving
Absolute Value Function
Evaluating
Introductory Example: Solving
Absolute Value Inequalities with or
Absolute Value Inequality
Absolute Value Equations
Absolute Value Inequalities with or
What does the absolute value of a number represent?
Two numbers are opposites, such as and . What is true about their absolute values?
Match each absolute value expression with its distance from on the number line.
Which of the following defines the absolute value of a number?
Arrange the steps in the correct order to find the absolute value of a number using a number line.
The absolute value of a number represents its _____ from on the number line.
Match each absolute value term or symbol with its meaning.
The absolute value of a number is its distance from on the number line.
Explain what absolute value means on a number line. Why is the absolute value of a number never negative? Finally, explain why opposite numbers like and have the same absolute value.
Learn After
In technical professions such as aerospace engineering, absolute value inequalities are used to define safety envelopes and acceptable tolerances. According to the standard algebraic definition, which of the following compound inequalities is equivalent to the absolute value inequality (where is a positive constant)?
In precision manufacturing, technicians use absolute value inequalities to define 'tolerances'—the allowable deviation from a target measurement. Match each symbolic inequality with the verbal description of the manufacturing standard it represents.
An HVAC technician uses the expression to monitor a building's climate control system, where represents the current temperature in degrees Fahrenheit. True or False: This mathematical statement is classified as an absolute value inequality because it contains an absolute value expression and an inequality symbol.
A laboratory technician is following a Standard Operating Procedure (SOP) to solve an absolute value inequality for an equipment calibration. Arrange the following steps in the correct logical order to solve an inequality of the form algebraically.
Quality Control and Mathematical Classification
Identifying Absolute Value Inequalities in Quality Control
A quality control technician at an automotive assembly plant monitors the precision diameter of steel pins. The engineering blueprint specifies that the acceptable diameter , in inches, must satisfy the mathematical statement . Because this mathematical statement includes an inequality sign and an absolute value expression, it is classified as an ____.