Evaluate each expression. -|-12|

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. Identify the inner absolute value: \(|-12|\). Since \(-12\) is negative, its absolute value is the positive counterpart, which is \(12\).
3. Rewrite the expression by replacing the inner absolute value with its value: \(- | -12 | = - 12\).
4. Now, evaluate the remaining expression, which is the negative of \(12\).
5. Conclude that the value of the expression is the negative of the absolute value of \(-12\).

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, |−12| equals 12 because distance is always positive regardless of direction.

Nested Absolute Values

When absolute value symbols are nested, such as -|-12|, evaluate the innermost absolute value first. This means finding the absolute value inside before applying any other operations outside.

Order of Operations

Order of operations dictates the sequence in which parts of an expression are evaluated. Here, absolute values are evaluated first, then the negative sign outside is applied to the result.