In Exercises 67–74, express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. -26 and -3

Verified step by step guidance

1. insert step 1> Identify the two numbers given in the problem: -26 and -3.
2. insert step 2> To find the distance between two numbers on a number line, use the formula for distance: |a - b|, where a and b are the two numbers.
3. insert step 3> Substitute the given numbers into the formula: |-26 - (-3)|.
4. insert step 4> Simplify the expression inside the absolute value: |-26 + 3|.
5. insert step 5> Evaluate the absolute value expression to find the distance.

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, |x| is equal to x if x is positive or zero, and -x if x is negative. This concept is crucial for understanding how to express distances between numbers.

Distance Between 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 allows us to quantify how far apart the two numbers are, which is essential for solving problems involving distances.

Evaluating Absolute Value Expressions

Evaluating absolute value expressions involves substituting values into the expression and simplifying it to find the numerical distance. For example, to evaluate |x|, you determine whether x is positive or negative and then apply the definition of absolute value. This step is necessary to find the actual distance between the given numbers, which in this case are -26 and -3.