1Cademy - Absolute Value Equations

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Absolute Value
Algebraic Equation

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Absolute Value Equations

For any algebraic expression $u$ and any positive real number $a$ , the condition $|u| = a$ means that the mathematical statement can be rewritten as two equivalent equations: $u = -a$ or $u = a$ . This property stems from the fact that we are seeking all values whose distance from zero is $a$ , and both $a$ and $-a$ satisfy this requirement. A single statement for the solutions can also be written as $u = \pm a$ . Remember that an absolute value cannot be a negative number.

Updated 2026-06-03

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OpenStax Intermediate Algebra
OpenStax Intermediate Algebra

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Equations with Two Absolute Values
Procedure for Solving an Absolute Value Equation
As an inventory analyst, you are reviewing an automated stock discrepancy report. The software uses absolute value equations to flag out-of-bounds inventory levels. You notice an error log containing the equation $|u| = -15$ . Recalling the fundamental properties of absolute value equations, what is the correct interpretation of this mathematical statement?
In a precision manufacturing facility, deviations from a target dimension are tracked using absolute value equations. As a quality control technician, you must interpret sensor readings to determine the possible values of a measurement $x$ . Match each absolute value statement below with its correct mathematical interpretation or solution.
In a facilities management role, you are monitoring a pressure sensor that triggers an alert when the pressure $P$ satisfies the absolute value equation $|P - 100| = 15$ psi. True or False: According to the algebraic properties of absolute value, this equation is equivalent to the two statements $P - 100 = 15$ or $P - 100 = -15$ .
Properties and Conditions of Absolute Value Equations
As a quality control technician, you are tasked with interpreting sensor readings using absolute value equations. To solve the equation $|u| = a$ , where $u$ represents a measurement deviation and $a$ is a positive tolerance limit, arrange the following steps in the correct logical sequence based on the definition of absolute value.
In a precision manufacturing facility, a quality control assistant monitors part thickness specifications using absolute value equations. According to the standard operating procedures, solving the tolerance equation $|u| = a$ (where $a$ is a positive real number) requires splitting it into two equivalent linear equations: $u = a$ or $u =$ ____.
Cold Storage Temperature Monitoring Alerts

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