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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1:27 minutes

Problem 15

Textbook Question

Evaluate each expression. -|-3|

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, so it is always non-negative.

Evaluate the absolute value of -3, which is written as |-3|. Since absolute value makes the number positive, |-3| becomes 3.

Now, consider the negative sign outside the absolute value, which is -|-3|.

Apply the negative sign to the result of the absolute value, which means you take the negative of 3, resulting in -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, 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, 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 |-3| requires recognizing that we are finding the absolute value of -3, which leads to a straightforward calculation.

Properties of Absolute Value

Absolute value has specific properties that are useful in algebra. One key property is that |a| = a if a is non-negative, and |a| = -a if a is negative. This property helps in simplifying expressions and solving equations involving absolute values, ensuring that the results remain consistent with the definition of distance.