In Exercises 1–12, find each absolute value.|4|

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 the absolute value is always non-negative.
3. Identify the number inside the absolute value bars, which is 4 in this case.
4. Since 4 is already a positive number, the absolute value of 4 is simply 4.
5. Conclude that the absolute value of |4| is 4.

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. For instance, |a| is always non-negative, meaning it is either zero or positive. Additionally, the absolute value of a product is the product of the absolute values, |ab| = |a| * |b|, and the absolute value of a sum satisfies the triangle inequality: |a + b| ≤ |a| + |b|.

Evaluating Absolute Value

To evaluate the absolute value of a number, you simply determine its distance from zero. For example, to find |4|, since 4 is positive, the absolute value is 4 itself. If the number were negative, such as |-4|, the absolute value would also be 4, demonstrating that absolute value always yields a non-negative result.