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

Verified step by step guidance

1. Recall that the distance between two points p and q on a number line can be expressed using the absolute value of their difference, which is \(|p - q|\).
2. Since the problem states that the distance between p and q is 2 units, set the absolute value expression equal to 2: \(|p - q| = 2\).
3. Alternatively, you can also write the equation as \(|q - p| = 2\) because absolute value measures distance and is symmetric.
4. This equation means that the difference between p and q is either 2 or -2, capturing both possible positions of p relative to q.
5. Thus, the absolute value equation \(|p - q| = 2\) correctly represents the distance between p and q being 2 units.

Key Concepts

Absolute Value as Distance

The absolute value of a number represents its distance from zero on the number line, always as a non-negative value. In algebra, |x - y| denotes the distance between points x and y, regardless of their order.

Distance Between Two Points on a Number Line

The distance between two points p and q on a number line is given by the absolute value of their difference, |p - q|. This formula ensures the distance is positive and measures how far apart the points are.

Formulating Equations with Absolute Value

To express a condition involving distance, such as 'distance is 2 units,' we set the absolute value expression equal to that number. For example, |p - q| = 2 states that the distance between p and q is exactly 2 units.