Evaluate each expression. -|7/2|

Verified step by step guidance

1. Identify the absolute value expression: \(|\frac{7}{2}|\).
2. Recall that the absolute value of a number is its distance from zero on the number line, which is always non-negative.
3. Evaluate the absolute value: \(|\frac{7}{2}| = \frac{7}{2}\).
4. Apply the negative sign outside the absolute value: -\(\frac{7}{2}\).
5. The expression simplifies to the negative of the absolute value result.

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, |7/2| equals 7/2, while |-7/2| also equals 7/2, illustrating that both positive and negative values yield the same absolute value.

Evaluating 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 -|7/2| requires first finding the absolute value of 7/2, which is 7/2, and then applying the negative sign to arrive at the final result of -7/2.

Negative Sign in Expressions

A negative sign in front of a number or expression indicates that the value is to be taken as its opposite. In the expression -|7/2|, the negative sign modifies the result of the absolute value operation, changing the positive outcome of 7/2 into -7/2. Understanding how to apply negative signs is crucial for accurate evaluation of mathematical expressions.