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 on a number line, say \( p \) and \( q \), is given by the absolute value of their difference: \( |p - q| \).
2. Since the problem states that the distance between \( p \) and \( q \) is 2 units, we can express this as \( |p - q| = 2 \).
3. Alternatively, the distance can also be written as \( |q - p| = 2 \) because absolute value ignores the order of subtraction.
4. Thus, the equation involving absolute value that represents the distance between \( p \) and \( q \) being 2 units is \( |p - q| = 2 \).
5. This equation means that the difference between \( p \) and \( q \) is exactly 2 units apart on the number line.

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, the absolute value of the difference between two points, |p - q|, measures the distance between p and q 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 reflects the actual separation between the points.

Formulating Equations with Absolute Value

To express a condition involving distance, such as 'the distance between p and q is 2 units,' we set the absolute value of their difference equal to 2: |p - q| = 2. This equation captures both cases where p is greater than q or vice versa.