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

Verified step by step guidance

1. Recognize that the expression involves the absolute value function, which returns the non-negative value of a number. The absolute value of a number \(x\) is denoted as \(|x|\) and is defined as \(|x| = x\) if \(x \geq 0\), and \(|x| = -x\) if \(x < 0\).
2. Start by evaluating the inner absolute value: calculate \(|-2|\). Since \(-2\) is negative, its absolute value is \(-(-2)\).
3. Simplify the inner absolute value: \(|-2| = 2\).
4. Now, evaluate the outer absolute value: \(|2|\). Since \(2\) is already positive, the absolute value remains \(2\).
5. Conclude that the value of the expression \(-|-2|\) is the negative of the inner absolute value, so it equals \(-2\).

Key Concepts

Absolute Value

The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. For example, |−2| equals 2 because −2 is two units away from zero.

Evaluating Expressions with Absolute Values

When evaluating expressions involving absolute values, first compute the absolute value part, then apply any remaining operations. For instance, in -|−2|, find |−2| = 2, then apply the negative sign to get -2.

Order of Operations

The order of operations dictates the sequence in which parts of an expression are evaluated. Absolute value is treated like parentheses and should be evaluated before applying multiplication, division, addition, or subtraction.