Learn Before
Introductory Example: Solving
To solve the introductory absolute value equation , one must find all numbers that make the mathematical statement true. Applying the geometric definition of absolute value, this requires finding all numbers whose distance from zero on the number line is exactly . Because both and are positioned exactly five units away from zero, they are both valid solutions. This means that if , then or . This pair of solutions can be conveniently simplified into a single mathematical statement by writing , which is read aloud as ' is equal to positive or negative '.
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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
A technician is monitoring a voltage level that must satisfy the condition . Based on the geometric definition of absolute value as the distance from zero on a number line, which values for satisfy this condition?
In a technical workshop, a sensor's offset must satisfy the equation . Match each mathematical term with its correct role or description in solving this problem.
A quality control inspector is checking the thickness deviation of a metal sheet relative to a standard baseline of millimeters. The deviation must satisfy the equation . Based on the geometric definition that this equation represents all points at a distance of units from zero, the two possible values for are and ____.
A technician is calibrating a sensor and needs to solve the equation to determine the allowable deviation from a center point of 0. Arrange the following steps in the correct logical order to solve this equation based on the geometric definition of absolute value.
Solving Absolute Value Deviations in Machining
A quality control technician is monitoring a machine's calibration deviation modeled by the absolute value equation . True or False: According to the geometric definition of absolute value, because distance on a number line can never be a negative value, is the only valid solution to this equation, and is an invalid solution.
Understanding Absolute Value Calibration Equations