Problem 67 - College Algebra

Question

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

Step-by-Step Solution

Answer

The distance between 2 and 17 is 15 units.

Step 1: Set Up the Absolute Value Expression

The distance between two numbers, a and b, on a number line can be obtained by the absolute value of their difference either \(|a - b|\) or \(|b - a|\). In this case, we need to calculate the distance between 2 and 17. Set it up as an expression: \(|2 - 17|\) or \(|17 - 2|\).

Step 2: Calculate the Inside of Absolute Value

Now calculate the difference. For \(|2 - 17|\), it will become \(|-15|\) and for \(|17 - 2|\), it'll become \(|15|\). Both these expressions represent the same distance.

Step 3: Evaluate the Absolute Value

The absolute value of -15 and 15 is 15. Therefore, the distance between 2 and 17 is 15 units.