Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 2 and 17

Verified step by step guidance

1. Identify the two numbers given: 2 and 17.
2. Recall that the distance between two numbers \(a\) and \(b\) on the number line can be expressed as the absolute value of their difference: \(\left| a - b \right|\).
3. Write the distance between 2 and 17 as \(\left| 2 - 17 \right|\) or equivalently \(\left| 17 - 2 \right|\).
4. Evaluate the expression inside the absolute value: calculate \(2 - 17\) or \(17 - 2\).
5. Find the absolute value of the result from the previous step to get the distance between the two numbers.

Key Concepts

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, e.g., |x|. For example, |−3| = 3 and |3| = 3.

Distance Between Two Numbers

The distance between two numbers on the number line is the absolute value of their difference. This ensures the distance is always positive or zero, calculated as |a − b|, where a and b are the given numbers.

Evaluating Absolute Value Expressions

To find the distance, substitute the numbers into the absolute value expression and simplify. For example, the distance between 2 and 17 is |2 − 17| = |−15| = 15, which gives the numerical distance.