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

Verified step by step guidance

1. Step 1: Understand the problem. We need to evaluate the expression -|4.5|.
2. Step 2: Recall the definition of absolute value. The absolute value of a number is its distance from zero on the number line, without considering direction. Therefore, |4.5| is simply 4.5.
3. Step 3: Apply the absolute value to the number inside the bars. So, |4.5| = 4.5.
4. Step 4: Apply the negative sign outside the absolute value. This means we take the negative of the result from Step 3.
5. Step 5: Combine the results from the previous steps to express the final evaluation as -4.5.

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|, and is always non-negative. For example, |4.5| equals 4.5, while |-4.5| also equals 4.5, illustrating that both positive and negative values yield the same absolute value.

Evaluation of Expressions

Evaluating an expression involves substituting values for variables and performing the necessary arithmetic operations to simplify the expression to a single numerical value. In this case, evaluating |4.5| requires recognizing that it is already in its simplest form, leading directly to the result without further calculations.

Properties of Absolute Value

Absolute value has several important properties, including |a| = a if a ≥ 0 and |a| = -a if a < 0. Additionally, the absolute value of a sum can be less than or equal to the sum of the absolute values, expressed as |a + b| ≤ |a| + |b|. Understanding these properties is essential for solving more complex problems involving absolute values.