Write an equation involving absolute value that says the distance between p and q is 2 units.

Verified step by step guidance

1. Understand that the absolute value represents the distance between two points on a number line.
2. The absolute value equation for the distance between two points $p$ and $q$ is given by $|p-q|$.
3. Set the absolute value equal to the distance, which is 2 units in this case.
4. Write the equation as $|p-q|=2$.
5. This equation states that the distance between $p$ and $q$ is 2 units.

Key Concepts

Absolute Value

Absolute value is a mathematical function that measures the distance of a number from zero on the number line, regardless of direction. It is denoted by two vertical bars, e.g., |x|. For any real number x, |x| = x if x is positive or zero, and |x| = -x if x is negative. This concept is crucial for understanding how distances are represented in equations.

Distance Formula

The distance formula calculates the distance between two points on a number line or in a coordinate system. In one dimension, the distance between two points p and q can be expressed as |p - q|. This formula is foundational for formulating equations that describe the relationship between points based on their distances.

Setting Up Equations

Setting up equations involves translating a verbal or conceptual statement into a mathematical expression. In this case, stating that the distance between p and q is 2 units translates to the equation |p - q| = 2. Understanding how to create and manipulate equations is essential for solving problems in algebra.