Express the distance between the numbers -17 and 4 using absolute value. Then evaluate the absolute value.

Verified step by step guidance

1. Recall that the distance between two numbers on the number line can be expressed as the absolute value of their difference. So, the distance between -17 and 4 is \(\left| -17 - 4 \right|\) or equivalently \(\left| 4 - (-17) \right|\).
2. Write the expression for the distance using absolute value: \(\left| -17 - 4 \right|\).
3. Simplify inside the absolute value: calculate \(-17 - 4\) which is \(-21\), so the expression becomes \(\left| -21 \right|\).
4. Recall the definition of absolute value: \(\left| x \right|\) is the distance of \(x\) from zero on the number line, which is always non-negative.
5. Evaluate the absolute value: \(\left| -21 \right|\) equals 21, which is the distance between -17 and 4.

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, 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. It is calculated as |a - b|, ensuring the result is non-negative and reflects the actual gap between the points, regardless of their order.

Evaluating Absolute Value Expressions

To evaluate an absolute value expression, first compute the value inside the bars, then take its non-negative magnitude. For example, | -21 | equals 21 because the distance from zero is 21, even though the number is negative.