In Exercises 1–12, find each absolute value.|-7.6|

Verified step by step guidance

1. Understand that the absolute value of a number is its distance from zero on the number line, regardless of direction.
2. Recognize that absolute value is always non-negative.
3. Identify the given number inside the absolute value symbols: -7.6.
4. Since -7.6 is negative, the absolute value will be the positive version of this number.
5. Therefore, the absolute value of |-7.6| is the positive counterpart of -7.6.

Key Concepts

Absolute Value

Absolute value is a mathematical function that measures the distance of a number from zero on the number line, regardless of direction. It is denoted by two vertical bars surrounding the number, such as |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.

Properties of Absolute Value

The absolute value function has several important properties. It is always non-negative, meaning |x| ≥ 0 for any real number x. Additionally, the absolute value of a product is the product of the absolute values, |xy| = |x||y|, and the absolute value of a sum is less than or equal to the sum of the absolute values, |x + y| ≤ |x| + |y|. These properties are useful in simplifying expressions and solving equations.

Evaluating Absolute Value

To evaluate the absolute value of a number, you determine its distance from zero. For example, to find |-7.6|, you recognize that -7.6 is less than zero, so you take the negative of it, resulting in 7.6. This process is straightforward and applies to any negative number, ensuring that the result is always a positive value or zero.