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

Key Concepts

Absolute Value Definition

Absolute value measures the distance of a number from zero on the number line, regardless of direction. For any real number x, the absolute value is denoted as |x| and is defined as |x| = x if x ≥ 0, and |x| = -x if x < 0. This concept is crucial for understanding how to express distances in mathematical terms.

Distance in Mathematics

In mathematics, distance can be represented as the absolute difference between two numbers. For example, the distance between a number r and a point a can be expressed as |r - a|. This principle is essential for formulating equations or inequalities that describe how far a number is from another number.

Inequalities and Equations

Inequalities express a relationship where one quantity is greater than or less than another, while equations state that two expressions are equal. In the context of absolute values, inequalities can represent conditions such as being 'no less than' a certain distance, which translates into mathematical expressions involving absolute values.