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

Key Concepts

Absolute Value

Absolute value is a mathematical concept that represents the distance of a number from zero on the number line, regardless of direction. It is denoted by two vertical bars, for example, |x|. For any real number x, the absolute value is defined as |x| = x if x is greater than or equal to zero, and |x| = -x if x is less than zero.

Distance Between Two Numbers

The distance between two numbers on the number line can be calculated using the absolute value of their difference. Specifically, the distance d between two numbers a and b is given by the formula d = |a - b|. This formula ensures that the distance is always a non-negative value, reflecting the concept of distance in a geometric sense.

Evaluating Absolute Value

Evaluating absolute value involves substituting a specific number into the absolute value expression and simplifying it. For example, to evaluate |x| for x = -17, you would find that |-17| = 17. This process is essential for solving problems that require finding distances or magnitudes, as it translates the abstract concept of distance into a concrete numerical value.