Evaluate each expression. -|7/2|

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Identify the expression to evaluate: \(-\left| \frac{7}{2} \right|\).

Recall that the absolute value \(|x|\) of a number \(x\) is the distance of \(x\) from zero on the number line, which is always non-negative.

Calculate the absolute value inside the expression: \(\left| \frac{7}{2} \right| = \frac{7}{2}\), since \(\frac{7}{2}\) is already positive.

Apply the negative sign outside the absolute value: \(-\left| \frac{7}{2} \right| = -\frac{7}{2}\).

Thus, the expression simplifies to the negative of the positive fraction \(\frac{7}{2}\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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, |7/2| equals 3.5, regardless of the sign of the original number.

Negative Sign Outside Absolute Value

When a negative sign is placed outside the absolute value, it means the negative of the absolute value. For instance, -|7/2| equals -3.5, which is the negative of the positive absolute value.

Evaluating Rational Numbers

Rational numbers are numbers expressed as a fraction of two integers. Evaluating expressions involving rational numbers requires simplifying fractions and applying operations like absolute value and negation correctly.

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