Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:48 minutes

Problem 16

Textbook Question

Evaluate each expression. -|-12|

Verified step by step guidance

Understand that the expression involves the absolute value function, which is denoted by the vertical bars | |.

Recall that the absolute value of a number is its distance from zero on the number line, regardless of direction, meaning it is always non-negative.

Identify the number inside the absolute value bars, which in this case is -12.

Apply the absolute value function: |-12|, which means you take the positive value of -12.

Conclude that the absolute value of -12 is 12, as the absolute value function converts negative numbers to their positive counterparts.

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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, regardless of direction. It is denoted by vertical bars, such as |x|, and is always non-negative. For example, |3| equals 3, and |-3| also equals 3. Understanding absolute value is crucial for evaluating expressions that involve negative numbers.

Evaluating Expressions

Evaluating an expression involves substituting values for variables and performing the necessary arithmetic operations to simplify it. In this case, the expression |-12| requires recognizing that the absolute value function transforms negative inputs into positive outputs. Mastery of this concept is essential for solving various mathematical problems.

Properties of Absolute Value

The properties of absolute value include the fact that |a| = a if a is non-negative, and |a| = -a if a is negative. Additionally, the absolute value of a product is the product of the absolute values, |ab| = |a||b|. These properties help in simplifying expressions and solving equations involving absolute values effectively.