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. Identify the two numbers given: -26 and -3.
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 -26 and -3 as \(\left| -26 - (-3) \right|\).
4. Simplify the expression inside the absolute value: \( -26 - (-3) = -26 + 3 \).
5. Evaluate the absolute value expression \(\left| -26 + 3 \right|\) to find the distance.

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. For example, |−3| = 3 and |3| = 3, showing that both are three units away from zero.

Distance Between Two Numbers

The distance between two numbers on the number line is the absolute value of their difference. This means the distance between numbers a and b is |a − b|, which ensures the result is non-negative and represents the length between the points.

Evaluating Absolute Value Expressions

To find the distance, first write the absolute value expression representing the difference between the two numbers. Then subtract the numbers inside the absolute value and simplify. Finally, take the absolute value to get the positive distance.