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

Verified step by step guidance

1. Identify the key phrase 'no less than 1 unit from 29', which indicates an absolute value situation.
2. Understand that 'no less than' means the distance is at least 1 unit away from 29.
3. Set up the absolute value inequality: $|r-29|\ge 1$.
4. This inequality states that the distance between $r$ and 29 is at least 1.
5. The solution involves finding all values of $r$ that satisfy this inequality.

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.