Evaluate each expression. See Example 5.-|-2|

Verified step by step guidance

1. Identify the expression: \(-|-2|\).
2. Understand that the vertical bars \(|\cdot|\) represent the absolute value, which makes any number inside them non-negative.
3. Calculate the absolute value of \(-2\), which is \(|-2| = 2\).
4. Apply the negative sign outside the absolute value: \(-|2| = -2\).
5. The expression evaluates to \(-2\).

Key Concepts

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|. For example, |2| equals 2, and |-2| also equals 2. Understanding absolute value is crucial for evaluating expressions that involve negative numbers.

Evaluating Expressions

Evaluating an expression involves substituting values for variables and performing the necessary arithmetic operations to simplify it. In this case, the expression |-2| requires recognizing that the absolute value function transforms negative inputs into positive outputs. Mastery of this concept is essential for solving mathematical problems accurately.

Properties of Absolute Value

The properties of absolute value include the fact that |a| = a if a is non-negative, and |a| = -a if a is negative. Additionally, the absolute value of a product is the product of the absolute values, |ab| = |a||b|. These properties help in simplifying and solving expressions involving absolute values effectively.