Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 15

Chapter 1, Problem 15

Evaluate each expression. -|-3|

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Identify the expression to evaluate: \(-|-3|\). This involves the absolute value of -3, followed by applying a negative sign outside.

Recall that the absolute value of a number is its distance from zero on the number line, always non-negative. So, \(| -3 |\) equals 3.

Substitute the absolute value result back into the expression: \(- | -3 | = -3\).

Understand that the negative sign outside the absolute value changes the sign of the absolute value result, so the expression evaluates to the negative of 3.

Therefore, the expression simplifies to \(-3\).

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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, |−3| equals 3 because −3 is three units away from zero.

Negative Sign Outside Absolute Value

When a negative sign is placed outside the absolute value, it negates the result of the absolute value operation. For instance, -|−3| means first find |−3| = 3, then apply the negative sign to get -3.

Order of Operations

The order of operations dictates that expressions inside absolute value bars are evaluated first, followed by applying any external operations like negation. This ensures correct evaluation of expressions such as -|−3|.

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