Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. −2 and 5

검증된 단계별 안내

Identify the two numbers given: -2 and 5.

Recall that the distance between two numbers \(a\) and \(b\) on the number line can be expressed as the absolute value of their difference: \(\left| a - b \right|\) or \(\left| b - a \right|\).

Write the distance between -2 and 5 as an absolute value expression: \(\left| -2 - 5 \right|\) or \(\left| 5 - (-2) \right|\).

Evaluate the absolute value: \(\left| -7 \right| = 7\) or \(\left| 7 \right| = 7\), which gives the distance between the two numbers.

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주요 개념

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

Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is always non-negative and is denoted by vertical bars, for example, |x|. This concept helps measure how far apart two numbers are without considering which is larger.

Distance Between Two Numbers

The distance between two numbers on the number line is the absolute value of their difference. For numbers a and b, the distance is |a - b|, which ensures the result is non-negative and reflects the actual gap between the points.

Evaluating Absolute Value Expressions

To find the distance, first write the absolute value expression representing the difference between the numbers. Then calculate the difference inside the bars and take its absolute value, converting any negative result to positive to get the final distance.