In Exercises 1–12, find each absolute value.|-7|

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: \(-7\).
4. Since \(-7\) is negative, the absolute value will be the positive version of this number.
5. Therefore, the absolute value of \(-7\) is the positive number that is 7 units away from zero.

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 can be less than or equal to the sum of the absolute values, |x + y| ≤ |x| + |y|, known as the triangle inequality.

Evaluating Absolute Value

To evaluate the absolute value of a number, you determine its distance from zero. For example, to find |-7|, you recognize that -7 is 7 units away from zero on the number line. Therefore, |-7| equals 7, illustrating that absolute value transforms negative numbers into their positive counterparts while leaving positive numbers unchanged.