Evaluate each expression. See Example 5. -|4.5|

Verified step by step guidance

1. Recognize that the expression involves the absolute value function and a negative sign outside it: \(- |4.5|\).
2. Recall that the absolute value of a number is its distance from zero on the number line, which is always non-negative. So, \(|4.5| = 4.5\).
3. Substitute the absolute value back into the expression: \(- |4.5| = - 4.5\).
4. Understand that the negative sign outside the absolute value changes the sign of the result, making it negative.
5. Therefore, the expression simplifies to \(-4.5\).

Key Concepts

Absolute Value

The absolute value of a number represents its distance from zero on the number line, regardless of direction. It is always non-negative, so |-4.5| equals 4.5. This concept is essential for evaluating expressions involving absolute value symbols.

Evaluating Numerical Expressions

Evaluating an expression means simplifying it to a single numerical value. For absolute value expressions, this involves identifying the number inside the bars and applying the absolute value operation correctly.

Notation and Symbols in Trigonometry

Understanding mathematical notation, such as the vertical bars for absolute value, is crucial. Recognizing these symbols helps correctly interpret and solve problems, especially when expressions include operations like absolute value.