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

검증된 단계별 안내

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 \(|p - q|\).

Since the problem states that the distance between p and q is 2 units, set the absolute value expression equal to 2: \(|p - q| = 2\).

Alternatively, you can also write the equation as \(|q - p| = 2\) because absolute value measures distance and is symmetric.

This equation means that the difference between p and q is either 2 or -2, capturing both possible positions of p relative to q.

Thus, the absolute value equation \(|p - q| = 2\) correctly represents the distance between p and q being 2 units.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.