Learn Before
Simplifying Absolute Value Expressions
To simplify an expression involving absolute value, determine the distance of the number inside the bars from zero:
- , because is three units from .
- , because is forty-four units from .
- , because is zero units from itself.
Since absolute value measures distance, the result is always the non-negative version of the number inside the bars. For a positive number or zero, the absolute value equals the number itself; for a negative number, the absolute value equals its opposite.
0
1
Tags
OpenStax
Elementary Algebra @ OpenStax
Ch.1 Foundations - Elementary Algebra @ OpenStax
Algebra
Math
Prealgebra
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 a warehouse inventory system, the absolute value of a stock discrepancy represents its distance from the expected count of zero. What is the absolute value of a discrepancy of -15 units?
In a manufacturing quality control system, a part that is 0.15 millimeters thinner than the standard is recorded with a deviation of -0.15. To report the magnitude of this error, the technician must simplify the absolute value expression |-0.15|. The result is ____.
In professional data analysis, absolute value is used to calculate the 'magnitude' of a deviation from a target, regardless of whether the recorded value was positive or negative. Match each absolute value expression representing a data variance to its simplified numerical magnitude.
In a professional logistics dashboard, a shipment that is 14 miles off-course is represented by the absolute value expression |-14|. True or False: To simplify this expression, you must determine the distance of -14 from zero, which results in a value of -14.
Calculating Magnitude of Financial Deviations
Justifying Magnitude in Shipping Reports
In a logistics operation, distance deviations from a central hub are recorded using absolute values to focus on the magnitude of the displacement. To simplify an absolute value expression like (representing a 35-mile deviation), arrange the following steps in the correct order according to the mathematical process of simplification.
Explaining Absolute Value in Professional Variance Reporting
In a professional construction project, a digital sensor is used to monitor the alignment of a structural beam. If the beam is perfectly aligned, the sensor records a deviation of 0. To find the magnitude of this deviation, the system simplifies the absolute value expression |0|. What is the result of this simplification?
Comparing Absolute Values and Integers
In a corporate project management dashboard, a task that is completed 10 days ahead of schedule is recorded as a variance of +10. To report the magnitude of this deviation, the system simplifies the absolute value expression |10|. What is the result of this simplification?
Simplifying