Write each statement using an absolute value equation or inequality. r is no less than 1 unit from 29.

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Identify the key phrase: "r is no less than 1 unit from 29" means the distance between r and 29 is at least 1.

Recall that the distance between two numbers r and 29 on the number line can be expressed using absolute value as \(|r - 29|\).

Translate "no less than 1 unit" into an inequality: the distance is greater than or equal to 1, so \(|r - 29| \geq 1\).

Write the absolute value inequality that represents the statement: \(|r - 29| \geq 1\).

This inequality means r is either at least 1 unit greater than 29 or at least 1 unit less than 29, capturing the original statement.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Absolute Value Definition

The absolute value of a number represents its distance from zero on the number line, always as a non-negative value. For any number x, |x| equals x if x is positive or zero, and -x if x is negative. This concept helps express distances regardless of direction.

Translating Distance Statements into Absolute Value

Statements about a variable being a certain distance from a number can be written as absolute value expressions. For example, 'r is no less than 1 unit from 29' translates to |r - 29| ≥ 1, where the absolute value measures the distance between r and 29.

Inequalities Involving Absolute Value

Absolute value inequalities describe ranges of values based on distance. An inequality like |x - a| ≥ b means the distance between x and a is at least b, so x lies outside the interval (a - b, a + b). Understanding this helps solve and graph such inequalities.

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