Table of contents

0. Review of Algebra4h 16m
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 19m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

1:23 minutes

Problem 57a

Textbook Question

In Exercises 51–60, rewrite each expression without absolute value bars. -3/|-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. Understanding absolute value is crucial for simplifying expressions that involve negative numbers.

Properties of Absolute Value

The properties of absolute value include that |a| = a if a is non-negative, and |a| = -a if a is negative. This means that when rewriting expressions involving absolute values, one must consider the sign of the number inside the absolute value bars. This property is essential for correctly simplifying expressions like -3/|-3|.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form, often by performing arithmetic operations and applying mathematical properties. In the context of the given expression, it requires substituting the absolute value with its equivalent based on the sign of the number. This skill is fundamental in algebra for solving equations and inequalities.