Non-negative Property of Absolute Value

Simplifying Absolute Value Expressions

Evaluating $|x|$, $|-y|$, and $-|u|$ 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 $|x| \leq 5$

Example: Solving $|x| < 7$

Try It: Solving $|x| < 9$ and $|x| < 1$

Example: Solving $|x| > 4$

Absolute Value Function

Evaluating $-|7|$

Introductory Example: Solving $|x| = 5$

Absolute Value Inequalities with $<$ or $\leq$

Absolute Value Inequality

Absolute Value Equations

Absolute Value Inequalities with $>$ or $\geq$

What does the absolute value of a number represent?

Two numbers are opposites, such as $5$ and $-5$. What is true about their absolute values?

Match each absolute value expression with its distance from $0$ 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 $n$ using a number line.

The absolute value of a number represents its _____ from $0$ on the number line.

Match each absolute value term or symbol with its meaning.

The absolute value of a number is its distance from $0$ on the number line.

Explain absolute value using a number line. Why are $|12|$ and $|-12|$ equal?

Try It: Solving $|x| < 9$ and $|x| < 1$

In a logistics monitoring system, a refrigerated shipping container is considered to be operating correctly if the temperature deviation $x$ (in degrees) satisfies the absolute value inequality $|x| < 7$. Which of the following intervals correctly represents the set of all acceptable temperature deviations in formal interval notation?

A quality control specialist at a manufacturing plant monitors the deviation $x$ (in millimeters) of a component's length from the standard specification. The component is considered 'within tolerance' if it satisfies the absolute value inequality $|x| < 7$. Match each representation of this tolerance range with its corresponding description.

A quality control technician defines the acceptable deviation $x$ of a machined part using the absolute value inequality $|x| < 7$. True or False: This condition is mathematically equivalent to the compound inequality $-7 < x < 7$.

A logistics analyst is preparing a training manual for warehouse staff to explain how to document shipping weight tolerances defined by the rule $|x| < 7$. Arrange the following steps in the correct order to solve this inequality and represent it in formal interval notation.

Maintenance Log: Compound Inequality Recording

During onboarding at a high-precision medical device manufacturing company, a quality control technician learns to record acceptable equipment deviations. The maximum allowable measurement deviation $x$ (in micrometers) of a surgical needle's thickness is represented by the absolute value inequality $|x| < 7$. To document this clearly in the daily log sheet using a compound inequality, the technician must translate this expression.

Complete the standard operating procedure statement:

'The abso

Standard Operating Procedure for Manufacturing Deviation Logs